Question

question 1625
16 what is the value of a in the triangle shown? use the law of cosines.
round your answer to the nearest integer.
a² = b² + c² - 2bc cos(a)
a) 6
b) 9
c) 16
d) 3

Explanation:

Step1: Identify Law of Cosines formula

$a^2 = b^2 + c^2 - 2bc\cos(A)$

Step2: Substitute values

$a^2 = 11^2 + 8^2 - 2(11)(8)\cos(32^\circ)$

Step3: Calculate squares and product

$a^2 = 121 + 64 - 176\cos(32^\circ)$

Step4: Compute cosine value

$\cos(32^\circ) \approx 0.8480$

Step5: Calculate 176×0.8480

$176×0.8480 ≈ 149.248$

Step6: Compute a²

$a^2 ≈ 185 - 149.248 = 35.752$

Step7: Find a

$a ≈ \sqrt{35.752} ≈ 6$ (nearest integer)

Answer:

A. 6