In an acute-angled triangle MPK, the height PH is 5√51 and the side PM is 50. Find the cos of the angle M.
| August 6, 2021 | education
Since PH is height, it is perpendicular to the MK side. This means that the MHP angle is 90.
It follows from this that the triangle MHP is right-angled.
According to the rules for finding the cosine in a right-angled triangle, we get: cos M = MH / PM.
We know the PM length, it remains to calculate the MH length.
It is known that in a right-angled triangle the sum of the squares of the legs is equal to the square of the hypotenuse, which means PM ^ 2 = MH ^ 2 + PH ^ 2.
Substitute the values and get: 50 ^ 2 = MH ^ 2 + (5√51) ^ 2.
MH ^ 2 = 50 ^ 2 – (5√51) ^ 2.
MH ^ 2 = 2500 – 52 * 51.
MH ^ 2 = 2500 – 25 * 51.
MH ^ 2 = 2500 – 1275.
MH ^ 2 = 1225.
MH = 35.
Now we can calculate cos M = 35/50.
cos M = 7/10.
cos M = 0.7.
Answer: cos M = 0.7.
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