Question

If A = 39°, ∠BDC = 50°, and AB = 48, find h (height), then x (unknown length). (Round each answer to the nearest whole number.)

a) h = 36, x = 25
b) h = 42, x = 30
c) h = 38, x = 28
d) h = 45, x = 35

Answer 1

To find the height, h, we can use trigonometric ratios. Since we have the angle A and the length AB, we can use the sine ratio. To find x, we can use the Law of Sines. The Law of Sines states that the ratio of the lengths of the sides of a triangle to the sines of their opposite angles is the same for all sides and angles.

Step-by-step explanation:

To find the height, h, we can use trigonometric ratios. Since we have the angle A and the length AB, we can use the sine ratio. In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. So, we can set up the equation sin(A) = h / AB and solve for h.

To find x, we can use the Law of Sines. The Law of Sines states that the ratio of the lengths of the sides of a triangle to the sines of their opposite angles is the same for all sides and angles. We can set up the equation sin(A) / AB = sin(B) / x and solve for x.

Using the given values, we have sin(39°) = h / 48, which gives us h ≈ 36. For x, we have sin(39°) / 48 = sin(50°) / x, which gives us x ≈ 25.