Question

Find the measure of angleq, the smallest angle in a triangle whose sides have lengths 4, 5, and 6. round the measure to the nearest whole degree. 34° 41° 51° 56°

Answer 1

The measure of the ∠Q = 41°

By law of cosines:

a law in trigonometry: the square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.

Which can we stated as:

${q}^2 = {p}^2 + {r}^2 - 2prcos(Q)\\{4}^2 = {6}^2 + {5}^2 - 2*6*5*cos(Q)$

solving equation using normal algebra:

60cos(Q) = 36 + 25 - 16

60 cos(Q) = 45

cos(Q) = 45/60

cos(Q) = 3/4

$Q = {cos}^{-1} (\frac{3}{4})$

Thus, Q = 41°

Hence, the measure of the smallest angle in a triangle whose sides have lengths 4, 5, and 6. ∠Q is 41°.

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