Question

The figure below shows two right triangles drawn at 90° to each other. Redraw the figure below, label it as the problem indicates, and then solve the problem. angle ABD=52^ C=43^ , BC = 29 , find x and then find h. (Round each answer to the nearest whole number.)

Answer 1

Based on the diagram of the two right triangles, the value of x and h include;

x = 27°.

h = 35°.

In order to determine the value of x, we would apply the tangent trigonometric function because the required and given side lengths represent the adjacent side and opposite side of a right-angled triangle respectively.

tan(θ) = Opp/Adj

Where:

• Adj represents the adjacent side of a right-angled triangle.
• Opp represents the opposite side of a right-angled triangle.
• θ represents the angle.

For the right-angled triangle ABC, we have the following equation for tanC:

tan(C) = AB/BC

tan(43°) = x/29

x = 29 × Tan(43°)

x = 29 × 0.9325

x = 27.0425 ≈ 27°

For the right-angled triangle ABD, we have the following equation for tanB:

tan(52°) = h/27

h = 27 × tan(52°)

h = 27 × 1.2799

h = 34.5573 ≈ 35°

Answer 2

1. x = 27

2. h = 35

Explanation:

From the question given above, the following data were obtained:

<ABD = 52°

Angle C = 43°

Line BC = 29

x =..?

h =...?

1. Determination of the value of x.

Angle C = 43°

Line BC = 29

x =..?

Using Tan ratio, the value of x can be obtained as follow:

Opposite = x

Adjacent = Line BC = 29

Angle C = 43°

Tan C = Opposite /Adjacent

Tan 43° = x/29

Cross multiply

x = 29 × Tan 43°

x = 29 × 0.9325

x = 27.0425 ≈ 27

x = 27

2. Determination of the value of h.

<ABD = 52°

x = 27

h =...?

Using Tan ratio, the value of h can be obtained as follow:

<ABD = 52°

Adjacent = x = 27

Opposite = h

Tan <ABD = Opposite /Adjacent

Tan 52° = h/27

Cross multiply

h = 27 × Tan 52

h = 27 × 1.2799

h = 34.5573 ≈ 35

h = 35