Question

What is the measure of ∠F, to the nearest degree?

Answer 1

Three lines given -- it's a natural for the cos(theta) law. A small hint: I think  the preferred way of doing it is to use the cos(theta) law twice. It will give you a definite answer.

Find G first
g = 6 yd
h = 7 yd
f = 5 yards.

g^2 = h^2 + f^2 - 2*h*f*cos(G)
6^2 = 7^2 + 5^2- 2*7*5*cos(G)
36 = 49 + 25 - 70*Cos(G)
36 = 74 - 70*cos(G)
-48 = - 70 * cos(G) Divide by -70
-38/-70 = cos(G)
0.5429 = cos(G)
cos-1(0.5429) = G
G = 57.12

Now find H
h^2 = g^2 + f^2 - 2*g*f*cos(H)
7^2 = 5^2 + 6^2 - 2*5*6*cos(H)
49 = 25 + 36 - 60cos(H)
49 =61  - 60*cos(H) 
Cos(H) = -12 / - 60
Cos(H) = 0.2
H = cos-1(0.2)
H = 78.46

F  can be found because every triangle has 180 degrees
F + 78.46 + 57.12 = 180
F +  135.58 = 180
F = 180 - 135.58
F = 44.41

A <<<< Answer.

Answer 2

Answer:

A. $44^{\circ}$

Step-by-step explanation:

We have been given a triangle FGH, we are asked to find the measure of angle F.

We will use law of cosines to solve our given problem.

$c^2=a^2+b^2-2ab\times \text{cos}(C)$, where, a, b and c are sides of triangle and C is the angle opposite to side c.

Upon substituting our given values in above formula we will get,

$5^2=7^2+6^2-2*7*6\times \text{cos}(F)$

$25=49+36-84\times \text{cos}(F)$

$25=85-84\times \text{cos}(F)$

$25-85=85-85-84\times \text{cos}(F)$

$-60=-84\times \text{cos}(F)$

$\frac{-60}{-84}=\frac{-84\times \text{cos}(F)}{-84}$

$\frac{5}{7}=\text{cos}(F)$

Now we will use arccos to solve for measure of angle F.

$F=\text{cos}^{-1}(\frac{5}{7})$

$F=44.415308597^{\circ}\approx 44^{\circ}$

Therefore, the measure of angle F is 44 degrees and option A is the correct choice.