Question

Red maple trees can reach heights of up to 80 feet. What is thw height of the maple tree shown below? Round up to the nearest tenth if necessary.

Answer 1

54.5

Explanation:

Okay, here we have this:

Considering the provided figure and information, we are going to calculate the requested measure, so we obtain the following:

We can see that the triangle is a right triangle, so we can use the trigonometric ratios.

So, we know an angle, the hypotenuse of the triangle and we want to find its opposite leg, therefore the trigonometric ratio that we must use is the sine since it relates these three measures, and we obtain:

Now, let's solve for h:

Finally we obtain that the correct answer is 54.5

Answer 2

Okay, here we have this:

Considering the provided figure and information, we are going to calculate the requested measure, so we obtain the following:

We can see that the triangle is a right triangle, so we can use the trigonometric ratios.

So, we know an angle, the hypotenuse of the triangle and we want to find its opposite leg, therefore the trigonometric ratio that we must use is the sine since it relates these three measures, and we obtain:

`sin\lparen35)=(h)/(95)`

Now, let's solve for h:

`\begin{gathered} h=sin\left(35\right?*95 \\ h\approx54.5ft \end{gathered}`

Finally we obtain that the correct answer is the third option.