Question

(PLEASE ANSWER!! I REALLY NEED HELP)

Answer 1

Answer:

A) 6.32 in.

B) 71.56°

C) 36.88°

Step-by-step explanation:

To solve each part of the problem, let's pay attention to the triangle ABC shown in the figure.

A) The slant height (l) of the cone is the hypotenuse of the right triangle ABC, then, to calculate it you can apply the Pythagorean Theorem:

$l=\sqrt{(AB)^{2}+(BC)^{2}}=\sqrt{(2in)^{2}+(6in)^{2}}=6.32in$

B) The angle asked is the angle ∠A, then, you have:

$tan^{-1}(A)=\frac{opposite}{adjacent}\tan^{-1}(A)=\frac{6}{2}$

∠$A=71.56$°

C) The angle formed between the segments (which you can call α) that represent the slant heights is twice the angle ∠C.

By definition, the sum of the interior angles of a triangle is 180°,so you can calculate the angle ∠C as following:

∠$C=180-90-71.56=18.44$

Then:

$\alpha=2*18.44$

$\alpha=36.88$°