Question

Can someone help with these trigonometry problems

Answer 1

4. What you want to do is first find the tan ratio, because tangent is opposite / adjacent, which you can use to find x.

So tan(52) = 1.28 ish. So we know that x/18 = 1.28.
Then multiply both sides by 18.

x / 18 * 18 = 1.28 * 18

x = about 23.

5. Now, you can use the pythagorean's theorem, a^2 + b^2 = c^2.

Just input all values.

18 ^ 2 + 23 ^ 2 = c ^ 2

324 + 529 = c ^ 2

853 = c^2

square root of 853 = c

x = 29.2 ish

6. In this case, use cosine, or adjacent / hypotenuse.

cos(16) = 0.96 ish

so that means 24/x = 0.96

Then basically,

24 / 0.96 = x

x = 25

So x = 25

Then you can use the Pythagorean's Theorem again. I'm not going to go as in depth.

a ^ 2 + b ^ 2 = c ^ 2

24 ^ 2 + b ^ 2 = 25 ^ 2

576 + b ^ 2 = 625

b ^ 2 = 49

b = 7

8. Use tan here. opposite/adjacent Again, not going as in depth.

tan(55) = 1.43 ish

1.43 = Y / 22

1.42 * 22 = Y

Y = 31.24 ish

Length of MN:

31.24 ^ 2 + 22 ^ 2 = c ^ 2

976ish + 484 = c ^ 2

1460 = c ^ 2

x = 38.2 ish

10. Use cosine.

cos(63) = about 0.45

Adjacent / hypotenuse

3 / x = 0.45

3 / 0.45= x

x = 6.67

And then pythagorean's Theorem.

6.67 ^ 2 = 3 ^ 2 + b ^ 2

44.5 = 9 + b ^ 2

35.5 = b^2

b = about 6