Question

What is the correct answer for this question ?

Answer 1

Answer:

$b)\ 61m$

Step-by-step explanation:

The given triangle is a right triangle. This means that one can use right-angle trigonometry to solve the triangle. The right angle trigonometric ratios are a set of ratios that relate the sides and angles of a triangle. These ratios are as follows,

$sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}$

Bear in mind, the names (opposite) and (adjacent) change depending on the angle of reference. However, the side (hypotenuse) refers to the side opposite the right angle, this side doesn't change depending on the reference angle.

In this problem, one is given the measure of an angle, and the measure of the hypotenuse, the problem asks one to solve for the side opposite the given angle measure. It would make the most logical sense to use the ratio of sine (sin) to do this.

$sin(\theta)=\frac{opposite}{hypotenuse}$

Substitute,

$sin(56)=\frac{h}{73}$

Inverse operations,

$sin(56)=\frac{h}{73}$

$73(sin(56))=h$

$60.519\approx h$