Question

In triangle mnp angle n = 90 degree nh is an alyiyude with point h on mp angle p = 21 degree and pm = 4cm find mh

a) 2.08 cm
b) 2.68 cm
c) 3.15 cm
d) 3.85 cm

Answer 1

To find the length of segment MH, use the trigonometric ratio sine. Then, use the Pythagorean theorem to calculate the length of MH. The length of segment MH is approximately 4.314 cm.

Step-by-step explanation:

To find the length of segment MH, we can use the trigonometric ratio sine. In triangle MNP, angle P = 21 degrees and PM = 4 cm. Since angle N is a right angle (90 degrees), we can use the sine of P to find the length of side MN.

Sine of angle P = Opposite / Hypotenuse

Sine(21 degrees) = MN / 4 cm

Using a calculator, we can find that the length of MN is approximately 1.43 cm.

Now, we can use the length of MN to find the length of MH. In triangle MHP, angle H is a right angle and side MP is known (4 cm). We can use the Pythagorean theorem to find the length of MH.

Pythagorean theorem: Hypotenuse^2 = Side1^2 + Side2^2

MH^2 = MP^2 + MN^2

MH^2 = 4^2 + 1.43^2

Using a calculator, we can find that the length of MH is approximately 4.314 cm.