Answer:
SL = 2.1 miles
Step-by-step explanation:
Given ∆LRS with RS extended to point T, and angles R = 35° and exterior angle LST = 70°, you want the measure of SL. You want to apply the process to finding distance to shore.
a. Isosceles triangle
The exterior angle LST is the sum of interior angles SRL and SLR. In equation form, this is ...
∠LST = ∠SRL +∠SLR
70° = 35° +∠SLR
∠SLR = 35°
The angles at either end of segment LR are both 35°, so the triangle is isosceles. That means sides SR and SL are congruent:
SL = SR = 2.1 miles
b. Distance to shore
The distance from the boat to the lighthouse has been found using an isosceles triangle. A similar method can be used to find the distance to shore. It requires the captain to be able to identify a point on shore, and measure the distance traveled parallel to the shore.
By using a 45° angle to start, and a 90° angle at the second measurement, the distance traveled between angle measurements will be exactly the (closest) distance to shore from the point of the second measurement.
Other angle measures can be used with trigonometric methods.
