Question

A scientist is trying to measure the distance across a marsh as shown in the figure above. He chooses two points at either end of the marsh representing the endpoints of the desired distance, D. He then chooses another point away from the marsh's border so that a right triangle is formed. He calculates that the angle between the base of this triangle and its hypotenuse is 45° . He then measures one of the sides of the triangle to be 300 m. What is the length, D, across the marsh? Round to the nearest tenth of a meter.
A.
212.1 m
B.
424.3 m
C.
600 m
D.
519.6 m

Answer 1

To solve this problem you must apply the proccedure shown below:
 1. You must apply the following trigonometric identity:
 $sin \alpha =opposite/hypotenuse$
 $\alpha =45 degrees$
 $opposite=300$
 $hypotenuse=D$
 2. When you substitute the values and solve for D, you obtain:
 $sin(45)=300/D$
 $D=300/sin(45)$
 $D=424.3 m$
 The answer is:$B. 424.3 m$