Question

In AMNO, the measure of angle O=90^ , the measure of angle M=64^ , and NO = 70 feet. Find the length of to the nearest tenth of a foot.

Answer 1

Trigonometry

Initial explanation

For a right triangle, depending on the location of the angle we are going to use, the sides receive different names:

This time, we have:

opposite side = 70 ft

hypotenuse = x

angle = 64º

Sine equation

We have that the equation of Sine is given by:

`\sin (\text{angle)}=\frac{\text{opposite}}{\text{hypotenuse}}`

Then, in this case:

`\sin (64º)=\frac{70\text{ ft}}{x}`

Since

sin(64º) = 0.89879

Then

`\begin{gathered} 0.89879=\frac{70\text{ ft}}{x} \\ \downarrow \\ 0.89879x=70\text{ ft} \\ \downarrow \\ x=\frac{70\text{ ft}}{0.89879}=77.88\text{ ft} \end{gathered}`

We want to find the nearest tenth of a foot, this means, our answer must have just one number after the decimal point.

Since 77.88 ≅ 77.9.

Then x = 77.9 ft

Answer: x = 77.9 ft