Question

In triangle MNP, measure of angle N is 90 degrees, NH is an altitude with point H on MP, measure of angle P is 21 degrees and PM is 4. Find MH

Answer 1

To find the length of segment MH in right-angled triangle MNP with angle N at 90 degrees and angle P at 21 degrees, we use the cosine function. The adjacent side MH over the hypotenuse MP is equal to cos(21°), which when solved gives MH approximately 3.73.

Step-by-step explanation:

The question involves finding the length of MH in right-angled triangle MNP with given measurements. Since angle N is 90 degrees and angle P is 21 degrees, by the trigonometry property in a right-angled triangle, we can use cosine to find MH.

Using the cosine of angle P:

cos(P) = Adjacent / Hypotenuse

= MH / MP

Since MP is given as 4, we have:

cos(21°) = MH / 4

Multiplying both sides by 4 to solve for MH:
4 * cos(21°) = MH

MH ≈ 4 * 0.93358

MH ≈ 3.73432

Therefore, the length of MH is approximately 3.73.