8. So here, you know the angle of elevation and the adjacent, and you're looking for the opposite. So first, put the angle into a tan calculator, because tan is the opposite/adjacent.
What you get is 8.64 ish.
So now, since you know the adjacent, just multiply the two together.
8.64 * 20 = 172.8, or about 173.
9. a. You can use the pythagorean's theorem to find this, or a ^ 2 + b ^ 2 = c ^ 2.
Basically, as long as you know the two legs' lengths in a right triangle, or a and b, you can find the hypotenuse, or c.
The two legs' lengths are 35 and 58.
So 35 ^ 2 + 58 ^ 2 = c ^ 2
1225 + 3364 = c ^ 2
4589 = c ^ 2
Then, you can square root both sides
= c
About 68 = c
68 km
b. To do this, just divide the two together, to find the ratio of opposite / hypotenuse (sin), or 58 / 68, which equals about 0.85
Put that in the sin ^ -1 in a calculator to get about 58.211, or 58 degrees.
10. I'm sure there's a more efficient way to do this that I don't know about but I'm stupid.
a. Whelp, me not knowing how to find the angle of indication/elevation leads to me just using tan because why not. 3.83 is about the answer, or 4.
b. Just multiply 15 by 15, to get 225 m.
11. umm, is there a b to this question?
a: sorry I don't know how to do this one :(
12. a. pythagorean's theorem, a ^ 2 + b ^ 2 = 5.6 ^ 2
Or a ^ 2 + b ^ 2 = 31.36
Since a = b,
a ^ 2 + a ^ 2 = 31.36
= 31.36
/2 /2
a ^ 2 = 15.68
a =
about 3.96 = a
3.96 + 3.96 + 5.6 = 13.52
b. Use sin here. 28 degrees in one of those sin calculators is 0.47.
That means the opposite / hypotenuse = 0.47.
So just multiply 0.47 by the hypotenuse, or 10.7, to get about 5.
So the short side of the rectangle is 5.
So you can either do the same with cosine or use the pythagorean's theorem. Either way, you should get about 9.4.
So the perimeter is 5 + 5 + 9.4 + 9.4 = 28.8 (ish)
13. To find the outside length of one of the four triangles or the hypotenuse, since you know the opposite, use sine. Sine is opposite / hypotenuse. 50 degrees in a sin thing is about 0.77. So that means 1.4 / hypotenuse = 0.77, or 1.4 / 0.77, which equals about 1.82.
So the length of the hypotenuse is about 1.82. That times 4 is 7.28, or about 7.3.
14. I'm sorry I don't know how to do this one, I can try tho :(
