I need help with these two questions about triangles

Question

I have two questions been torturing me since yesterday, I tried to use the law of sines, but I couldn't. to be real, I really don't understand what these quotations want me to do.

The first question

https://www9.0zz0.com/2023/03/15/17/732736977.png

The second question

https://www9.0zz0.com/2023/03/15/17/664989807.png

Answer 1

First question:

Using the fact that ∠α is supplementary to 87.9°, ∠α = 92.1°

Using the fact that the sum of the interior angles of a triangle is 180°, ∠β = 4.5°

Then use the Law of Sines:

sin(4.5°)/47 = sin(83.4°)/d

d•sin(4.5°) = 47sin(83.4°)

d = 47sin(83.4°)/sin(4.5°) = 595.068 or 595 km

Now that you have that length, you can make a right triangle by coming straight down from the satellite and use SOHCAHTOA trig ratios to solve for the height.

sin(87.9) = h/595.068

h = 595.068•sin(87.9) = 594.7 km

For the second problem, follow the same sort of process.

Answer 2

In the first problem you are given an exterior an angle of the triangle. From Geometry, the exterior angle is equal to the sum of the remote interior angles. so,

87.9 = 83.4 + x where x is the measure of the angle at the top of the triangle

x = 4.5^o

^{Once you have that angle, you can use the law of sines to solve the triangle.}

^{In the second problem, you are given 2 angles of the triangle. The sum of all angles = 180, so the third angle must be 54. Then use the Law of the signs to find the other 2 sides.}

Let me know if you need futher help with these.