Question

Let (theta) be the angle of elevation from point on the ground to the top of a tree. If cos (theta)=11/61 and the distance from the point on the ground to the base of the tree is 22ft, then how tall is the tree?

Answer 1

If you know your SOHCAHTOA then you know that

\(\cos\theta = \dfrac{adj}{hyp} =\dfrac{22~ft}{hyp} \)

We are told

\(\cos \theta = \dfrac{11}{61} \)

That means

\(\dfrac{22~ft}{hyp} = \dfrac{11}{61 } \)

We can solve for the hypotenuse:

\(hyp = \dfrac{61 \times 22~ft }{11} = 122 ~ft\)

Answer 2

Now you can use the sine or the Pythagorean theorem to find the height of the tree.

Answer 3

\[x^{2}+y ^{2}= r ^{2}\]
right?

Answer 4

yes

Answer 5

Thank you so much for taking the time. :)

Answer 6

You're welcome.