Question

Q5 Q30.) Find the measure of the side of the right triangle whose length is designated by a lowercase letter b. Round answers to the nearest whole number.

Answer 1

This answer can be found using cosine.  Cosine is the length of the adjacent side divided by the length of the hypotenuse from the viewpoint of theta.  In this problem, the 37° angle is theta, the hypotenuse is 238 in, and the adjacent side will be represented by x.  The equation would be set up as follows: cos(37)=x/238.  To find x, use basic algebra to multiply each side by 238 to get x=238cos(37).  Next, plug this into a calculator to get ≈182.  Side b is 182 inches.

Answer 2

The measure of the side of the right triangle whose length is designated by the lowercase letter b is approximately 143 inches.

To determine the value of b, we can use the trigonometric sine function (sin) and the Pythagorean theorem.

The sine function relates the sides of a right triangle as follows: sin(angle) = opposite side / hypotenuse.

In this case, we know the angle (A = 37 degrees) and the hypotenuse (AB = 238 inches). We need to find the opposite side (AC = b).

Using the sine function, we can write:

sin(37 degrees) = AC / AB

Substituting the known values, we get:

sin(37 degrees) = b / 238 inches

Multiplying both sides of the equation by 238 inches, we get:

b = 238 inches * sin(37 degrees)

Using a calculator, we can find that:

b ≈ 143 inches

Therefore, the measure of the side of the right triangle whose length is designated by the lowercase letter b is approximately 143 inches.