Draw a diagram for this situation and then use the Law of Sines.
≈ 90.2 ft
Practice makes perfect
Let's recall that the Law of Sines relates the sine of each angle to the length of the opposite side. For any △ ABC, let the lengths of the sides opposite angles A, B, and C be a, b, and c, respectively.
By the Law of Sines, we can write the following equation.
sin A/a=sin B/b=sin C/c
In our case, we know that a 125-foot redwood tree is leaning 20^(∘) off vertical. We want to calculate the length of the shadow if the angle the sunlight makes with the ground is 68^(∘). Let's create a diagram for this situation. Let x represent the length for which we are looking.
Note that the angle opposite to x is 180^(∘) minus the measures of the two other angles.
180^(∘)-70^(∘)-68^(∘)= 42^(∘)
Let's add this information to our diagram.
Let's write the equation according to the Law of Sines, and then solve it!
