Exercise 14 Page 603

We know that Hokiri's ladder has two 8 feet long legs, which, when the ladder is opened for use, are 4 feet apart.

We want to find the angle that is formed by the legs of the ladder when the ladder is opened. To do so, we can approximate this situation using an isosceles triangle. The congruent sides will be 8 feet long, and the base will be 4 feet long. Let's also call the desired angle x.

Since our triangle is isosceles, a perpendicular bisector of the base intersects the top vertex, and the x angle is split in half. This results in the creation of two right triangles that are congruent to each other. The shorter leg of these triangles is half the base of the isosceles triangle, so its length is 4÷ 2 = 2 feet. Also, the hypotenuses will be 8 feet long.

Now, let's recall the definition of a sine ratio. sin θ = Opposite/Hypotenuse In our case, θ = x2, the opposite side is 2 feet long, and the hypotenuse is 8 feet long. Therefore, we can write the following equation for x. sin x/2 = 2/8 = 0.25 Now, let's isolate x on the left-hand side using the inverse sine and simplify.

sin x/2 = 0.25

sin^(-1)(LHS) = sin^(-1)(RHS)

x/2 = sin^(-1) (0.25)

MultEqn

LHS * 2=RHS* 2

x = 2 sin^(-1) (0.25)

UseCalc

Use a calculator

x = 28.955024...^(∘)

RoundDec

Round to 2 decimal place(s)

x ≈ 28.96^(∘)

The created angle is about 28.96^(∘).