Question

Okay I been on these 2 questions for about 30 min and I can't figure it out.

1:Jenna climbed a mountain and stood at the summit which was 4,000 feet above sea level. Mario is standing at sea level 3,000 feet from the base of the mountain and looking at Jenna through binoculars. What is Jenna's angle of elevation as seen from Mario’s vantage point? Enter your answer in degrees.
2:A cable runs from the top of a pole to a spot on the ground 10 feet from the base of the pole. The pole makes a right angle with the ground. If the cable is 20 feet long, what is the angle the cable makes with the ground? Enter your answer in degrees.

Answer 1

For #1 you have one leg of a right triangle measuring 4000 (the height of the mountain) and the other leg is 3000 (the distance that Mario is from Jenna). The angle of elevation is the one on the base of the triangle across from the right angle. To find the measure of the angle, use the tangent ratio: tan(A)=4000/3000, which could be simplified to tanA = 4/3. Do that on your calculator using the inverse tangent function to get that the angle of elevation from Mario to Jenna is 53 degrees.
For #2 you have another right triangle situation where the length of the hypotenuse is 20 and the base leg is 10. You are finding again the base angle across from the right angle. Use the cosA=10/20, aka cosA=.5. Again use the inverse cos function on your calculator to find the angle in question is 60 degrees.