Question

GEOMETRY 100 POINTS

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Answer 1

The height is 74.64 meters

Explanation:

We have a ΔABC with ∠B = 75°, hypotenuse = AB

`cos\; 75\textdegree = (√(3) -1)/(2√(2) )\\\\(1)/(cos\; 75\textdegree) = (2√(2) )/(√(3) -1)`

cos B = adjacent/hyppotenuse

⇒ hypotenuse (AB) = adjacent/cosB = 20/cosB

`= 20 (2√(2) )/(√(3) -1)\\\\= (40√(2) )/(√(3) -1)\\\\= 77.27`

⇒ AB = 77.27

By pythagoras theorem,

AB² = AC² + BC²

⇒ AC² = AB² - BC²

= 77.27² - 20²

AC² = 5570.65

⇒ AC = √5570.65

AC = 74.64

Answer 2

A.

Explanation:

In this case, we have to use tan (
`(opposite)/(adjacent)` because we are asked for the opposite side (x) given the adjacent side (20 m).

So tan(75)=
`(x)/(20)`

Solve for x

x = 20 * tan(75)

x = 74.641...

x = 74.64 m