Question

1.What is the length of the altitude of an equilateral triangle with side lengths of 34 inches?

2. The bottom of a ladder must be placed 10 feet from a wall and reach a height of 16 feet. How long is the ladder?

I need help pls

Answer 1

Explanation:

Remark

Question One

It's equilateral. All three sides are equal. The base is 34 as well. So two right angles can be formed on the base by dropping the altitude from the top vertex.

Givens

altitude = h

a = 34/2 = 17

hypotenuse = 34

Formula

a^2 + h^2 = c^2

Solution

17^2 + h^2 = 34^2

289 + h^2 = 1156

h^2 +289 =1156

h^2 = 1156 - 289

h^2 = 867

sqrt(h^2) = sqrt(867)

h = 29.444

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Question Two

Givens

b = 10 feet

c = ?

height = h = 16

Formula

c^2 = b^2 + h^2

Solution

c^2 = 10^2 + 16^2

c^2 = 100 + 256

c^2 = 356

sqrt(c^2) = sqrt(356)

c = 18.87