Question

What is the value of r? Enter your answer in the box. Round your final answer to the nearest whole number. r = units A right triangle has a horizontal leg labeled 12 with its opposite angle labeled 67.4 degrees. The hypotenuse is labeled r.

Answer 1

12 divided by sin(67.4) = 13

Answer 2

Answer: 13 units

Step-by-step explanation:

Given: A right triangle has a horizontal leg =12 units

The opposite angle to the horizontal leg = 67.4 degrees

In trigonometry, the value of sine of an angle (x) in a right triangle is given by:-

$\sin x=\frac{\text{side opposite to x}}{\text{Hypotenuse}}$

Since, the hypotenuse is labeled as r.

Then , we have

$\sin(67.4^{\circ})=\frac{12}{r}\\\\\Rightarrow\ r=\frac{12}{\sin (67.4^{\circ})}\\\\\Rightarrow r=\frac{12}{0.92321021711}\\\\\Rightarrow r=12.9981230467\approx13$

Hence, the value of r = 13 units.