Mixing
Use cosine rule to determine the length of a side of a triangle. Cannot replicate textbook solution
Given a triangle of lengths $4$, $5$ and $x$, where the sides of length $4$ and $5$ meet at an angle of $60^{circ}$, I must calculate the length of side $x$.
The cosine rule is: $$a^2 = b^2 + c^2 - 2bccos(alpha)$$
So, applying to my problem:
$$begin{align}
a^2&=b^2+c^2-2bccos(alpha) \
x^2&=4^2+5^2-2(4)(5)(cos(60^{circ})) \
x^2&=16+25-40cos(60^{circ}) \
x^2&=41-40cos(60^{circ}) \
x^2&=41-40(0.9524) \
x^2&=41-38.1 \
x^2&=2.9 \
x&=sqrt{2.9}
end{align}$$
The textbook solution says I should arrive at $x = sqrt{21}$, not $x=sqrt{2.9}$. The textbook does not provide working to the solution, only the final answer.
Where did I go wrong?
trigonometry triangle
edited Nov 20 '18 at 21:01
Robert Howard
1,9161822
asked Sep 21 '18 at 14:38
Doug Fir
2177
add a comment |
Given a triangle of lengths $4$, $5$ and $x$, where the sides of length $4$ and $5$ meet at an angle of $60^{circ}$, I must calculate the length of side $x$.
The cosine rule is: $$a^2 = b^2 + c^2 - 2bccos(alpha)$$
So, applying to my problem:
$$begin{align}
a^2&=b^2+c^2-2bccos(alpha) \
x^2&=4^2+5^2-2(4)(5)(cos(60^{circ})) \
x^2&=16+25-40cos(60^{circ}) \
x^2&=41-40cos(60^{circ}) \
x^2&=41-40(0.9524) \
x^2&=41-38.1 \
x^2&=2.9 \
x&=sqrt{2.9}
end{align}$$
The textbook solution says I should arrive at $x = sqrt{21}$, not $x=sqrt{2.9}$. The textbook does not provide working to the solution, only the final answer.
Where did I go wrong?
trigonometry triangle
edited Nov 20 '18 at 21:01
Robert Howard
1,9161822
asked Sep 21 '18 at 14:38
Doug Fir
2177
$cos 60°=0.5$, you need to study the unit circle
– Vasya
Sep 21 '18 at 14:57
add a comment |
Given a triangle of lengths $4$, $5$ and $x$, where the sides of length $4$ and $5$ meet at an angle of $60^{circ}$, I must calculate the length of side $x$.
The cosine rule is: $$a^2 = b^2 + c^2 - 2bccos(alpha)$$
So, applying to my problem:
$$begin{align}
a^2&=b^2+c^2-2bccos(alpha) \
x^2&=4^2+5^2-2(4)(5)(cos(60^{circ})) \
x^2&=16+25-40cos(60^{circ}) \
x^2&=41-40cos(60^{circ}) \
x^2&=41-40(0.9524) \
x^2&=41-38.1 \
x^2&=2.9 \
x&=sqrt{2.9}
end{align}$$
The textbook solution says I should arrive at $x = sqrt{21}$, not $x=sqrt{2.9}$. The textbook does not provide working to the solution, only the final answer.
Where did I go wrong?
trigonometry triangle
edited Nov 20 '18 at 21:01
Robert Howard
1,9161822
asked Sep 21 '18 at 14:38
Doug Fir
2177
Given a triangle of lengths $4$, $5$ and $x$, where the sides of length $4$ and $5$ meet at an angle of $60^{circ}$, I must calculate the length of side $x$.
The cosine rule is: $$a^2 = b^2 + c^2 - 2bccos(alpha)$$
So, applying to my problem:
$$begin{align}
a^2&=b^2+c^2-2bccos(alpha) \
x^2&=4^2+5^2-2(4)(5)(cos(60^{circ})) \
x^2&=16+25-40cos(60^{circ}) \
x^2&=41-40cos(60^{circ}) \
x^2&=41-40(0.9524) \
x^2&=41-38.1 \
x^2&=2.9 \
x&=sqrt{2.9}
end{align}$$
The textbook solution says I should arrive at $x = sqrt{21}$, not $x=sqrt{2.9}$. The textbook does not provide working to the solution, only the final answer.
Where did I go wrong?
trigonometry triangle
trigonometry triangle
edited Nov 20 '18 at 21:01
Robert Howard
1,9161822
asked Sep 21 '18 at 14:38
Doug Fir
2177
edited Nov 20 '18 at 21:01
Robert Howard
1,9161822
asked Sep 21 '18 at 14:38
Doug Fir
2177
edited Nov 20 '18 at 21:01
Robert Howard
1,9161822
edited Nov 20 '18 at 21:01
Robert Howard
1,9161822
edited Nov 20 '18 at 21:01
Robert Howard
1,9161822
1,9161822
asked Sep 21 '18 at 14:38
Doug Fir
2177
asked Sep 21 '18 at 14:38
Doug Fir
2177
asked Sep 21 '18 at 14:38
Doug Fir
2177
2177
$cos 60°=0.5$, you need to study the unit circle
– Vasya
Sep 21 '18 at 14:57
add a comment |
$cos 60°=0.5$, you need to study the unit circle
– Vasya
Sep 21 '18 at 14:57
$cos 60°=0.5$, you need to study the unit circle
– Vasya
Sep 21 '18 at 14:57
$cos 60°=0.5$, you need to study the unit circle
– Vasya
Sep 21 '18 at 14:57
add a comment |
1 Answer
1
active
oldest
votes
Hint: $cos(60^o)=0.5$ maybe you mixed radians ($60^o=1/3pi$) with degrees on your calculator?
edited Nov 20 '18 at 20:56
klirk
2,619530
answered Sep 21 '18 at 14:44
Nicky Hekster
28.2k53456
Oh. I used Google Calculator in my browser: google.com/search?q=online+calculator, I typed the COS button then 60. Thanks for letting me know. Are you able to get 0.5 with Googles online calculator somehow?
– Doug Fir
Sep 21 '18 at 14:55
Hm. I just openned R application too and typed cos(60) which gave me the same result as Google calculator
– Doug Fir
Sep 21 '18 at 14:57
2
@DougFir: In Google calculator, click "Rad" in the left top corner, that will switch it to degrees.
– Vasya
Sep 21 '18 at 14:59
@Vasya thank you, that allowed me to replicate the result 0.5.
– Doug Fir
Sep 21 '18 at 15:00
@DougFir $cos 60text{rad}approx -0.9524$, so there's a sign issue too. A negative cosine is obtained for obtuse angles.
– J.G.
Nov 20 '18 at 22:10
add a comment |
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1 Answer
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active
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Hint: $cos(60^o)=0.5$ maybe you mixed radians ($60^o=1/3pi$) with degrees on your calculator?
edited Nov 20 '18 at 20:56
klirk
2,619530
answered Sep 21 '18 at 14:44
Nicky Hekster
28.2k53456
Oh. I used Google Calculator in my browser: google.com/search?q=online+calculator, I typed the COS button then 60. Thanks for letting me know. Are you able to get 0.5 with Googles online calculator somehow?
– Doug Fir
Sep 21 '18 at 14:55
Hm. I just openned R application too and typed cos(60) which gave me the same result as Google calculator
– Doug Fir
Sep 21 '18 at 14:57
2
@DougFir: In Google calculator, click "Rad" in the left top corner, that will switch it to degrees.
– Vasya
Sep 21 '18 at 14:59
@Vasya thank you, that allowed me to replicate the result 0.5.
– Doug Fir
Sep 21 '18 at 15:00
@DougFir $cos 60text{rad}approx -0.9524$, so there's a sign issue too. A negative cosine is obtained for obtuse angles.
– J.G.
Nov 20 '18 at 22:10
add a comment |
Hint: $cos(60^o)=0.5$ maybe you mixed radians ($60^o=1/3pi$) with degrees on your calculator?
edited Nov 20 '18 at 20:56
klirk
2,619530
answered Sep 21 '18 at 14:44
Nicky Hekster
28.2k53456
Oh. I used Google Calculator in my browser: google.com/search?q=online+calculator, I typed the COS button then 60. Thanks for letting me know. Are you able to get 0.5 with Googles online calculator somehow?
– Doug Fir
Sep 21 '18 at 14:55
Hm. I just openned R application too and typed cos(60) which gave me the same result as Google calculator
– Doug Fir
Sep 21 '18 at 14:57
2
@DougFir: In Google calculator, click "Rad" in the left top corner, that will switch it to degrees.
– Vasya
Sep 21 '18 at 14:59
@Vasya thank you, that allowed me to replicate the result 0.5.
– Doug Fir
Sep 21 '18 at 15:00
@DougFir $cos 60text{rad}approx -0.9524$, so there's a sign issue too. A negative cosine is obtained for obtuse angles.
– J.G.
Nov 20 '18 at 22:10
add a comment |
Hint: $cos(60^o)=0.5$ maybe you mixed radians ($60^o=1/3pi$) with degrees on your calculator?
edited Nov 20 '18 at 20:56
klirk
2,619530
answered Sep 21 '18 at 14:44
Nicky Hekster
28.2k53456
Hint: $cos(60^o)=0.5$ maybe you mixed radians ($60^o=1/3pi$) with degrees on your calculator?
edited Nov 20 '18 at 20:56
klirk
2,619530
answered Sep 21 '18 at 14:44
Nicky Hekster
28.2k53456
edited Nov 20 '18 at 20:56
klirk
2,619530
edited Nov 20 '18 at 20:56
klirk
2,619530
edited Nov 20 '18 at 20:56
klirk
2,619530
2,619530
answered Sep 21 '18 at 14:44
Nicky Hekster
28.2k53456
answered Sep 21 '18 at 14:44
Nicky Hekster
28.2k53456
answered Sep 21 '18 at 14:44
Nicky Hekster
28.2k53456
28.2k53456
Oh. I used Google Calculator in my browser: google.com/search?q=online+calculator, I typed the COS button then 60. Thanks for letting me know. Are you able to get 0.5 with Googles online calculator somehow?
– Doug Fir
Sep 21 '18 at 14:55
Hm. I just openned R application too and typed cos(60) which gave me the same result as Google calculator
– Doug Fir
Sep 21 '18 at 14:57
2
@DougFir: In Google calculator, click "Rad" in the left top corner, that will switch it to degrees.
– Vasya
Sep 21 '18 at 14:59
@Vasya thank you, that allowed me to replicate the result 0.5.
– Doug Fir
Sep 21 '18 at 15:00
@DougFir $cos 60text{rad}approx -0.9524$, so there's a sign issue too. A negative cosine is obtained for obtuse angles.
– J.G.
Nov 20 '18 at 22:10
add a comment |
Oh. I used Google Calculator in my browser: google.com/search?q=online+calculator, I typed the COS button then 60. Thanks for letting me know. Are you able to get 0.5 with Googles online calculator somehow?
– Doug Fir
Sep 21 '18 at 14:55
Hm. I just openned R application too and typed cos(60) which gave me the same result as Google calculator
– Doug Fir
Sep 21 '18 at 14:57
2
@DougFir: In Google calculator, click "Rad" in the left top corner, that will switch it to degrees.
– Vasya
Sep 21 '18 at 14:59
@Vasya thank you, that allowed me to replicate the result 0.5.
– Doug Fir
Sep 21 '18 at 15:00
@DougFir $cos 60text{rad}approx -0.9524$, so there's a sign issue too. A negative cosine is obtained for obtuse angles.
– J.G.
Nov 20 '18 at 22:10
Oh. I used Google Calculator in my browser: google.com/search?q=online+calculator, I typed the COS button then 60. Thanks for letting me know. Are you able to get 0.5 with Googles online calculator somehow?
– Doug Fir
Sep 21 '18 at 14:55
Oh. I used Google Calculator in my browser: google.com/search?q=online+calculator, I typed the COS button then 60. Thanks for letting me know. Are you able to get 0.5 with Googles online calculator somehow?
– Doug Fir
Sep 21 '18 at 14:55
Hm. I just openned R application too and typed cos(60) which gave me the same result as Google calculator
– Doug Fir
Sep 21 '18 at 14:57
Hm. I just openned R application too and typed cos(60) which gave me the same result as Google calculator
– Doug Fir
Sep 21 '18 at 14:57
2
2
@DougFir: In Google calculator, click "Rad" in the left top corner, that will switch it to degrees.
– Vasya
Sep 21 '18 at 14:59
@DougFir: In Google calculator, click "Rad" in the left top corner, that will switch it to degrees.
– Vasya
Sep 21 '18 at 14:59
@Vasya thank you, that allowed me to replicate the result 0.5.
– Doug Fir
Sep 21 '18 at 15:00
@Vasya thank you, that allowed me to replicate the result 0.5.
– Doug Fir
Sep 21 '18 at 15:00
@DougFir $cos 60text{rad}approx -0.9524$, so there's a sign issue too. A negative cosine is obtained for obtuse angles.
– J.G.
Nov 20 '18 at 22:10
@DougFir $cos 60text{rad}approx -0.9524$, so there's a sign issue too. A negative cosine is obtained for obtuse angles.
– J.G.
Nov 20 '18 at 22:10
add a comment |
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$cos 60°=0.5$, you need to study the unit circle
– Vasya
Sep 21 '18 at 14:57