Question

A 25ft ladder is leaning against a building at an angle of elevation of 70°. How high up the building will the ladder reach?

Answer 1

Given:

There are given that the 25 ft ladder and angle is 70 degrees.

Explanation:

To find the height of the building, first, we need to draw the image:

Then, the image will be:

Now,

From the above figure, we need to find the value of x.

So,

To find the value of x, we need to use the sin function.

Then,

$sin70^{\circ}=\frac{AB}{AC}$

Then,

$\begin{gathered} s\imaginaryI n70^{\operatorname{\circ}}=\frac{AB}{AC} \\ s\imaginaryI n70^{\operatorname{\circ}}=\frac{x}{25} \\ x=sin70^{\circ}\times25 \\ x=23.5\text{ ft} \end{gathered}$

Final answer:

Hence, the height of the building is 23.5 ft.