Question

PLEASE HELP ME AND EXPLAIN!!!
Subject: Law of Cosines

Answer 1

Explanation:

just plug the numbers in to get your answer. c=90

a=55, b=50. so basically

(90)^2=(55)^2+(50)^2-2(55)(50)*cos90

Answer 2

32.7°

Explanation:

Cosine rule

`c^2=a^2+b^2-2ab \cos C`

Where:

• a, b and c are the sides of a triangle.
• C is the angle opposite side c.

From inspection of the given triangle:

• C = Y
• c = XZ = 55 ft
• a = XY = 50 ft
• b = YZ = 90 ft

Substitute the given values into the formula and solve for Y:

`\begin{aligned}c^2 & =a^2+b^2-2ab \cos C\\\implies 55^2 & = 50^2+90^2-2(50)(90) \cos Y\\3025 & = 2500+8100-9000 \cos Y\\9000 \cos Y & = 2500+8100-3025\\9000 \cos Y & =7575\\\cos Y & =(7575)/(9000)\\\cos Y & =(101)/(120)\\Y & =\cos^(-1) \left((101)/(120)\right)\\Y & = 32.68346376^(\circ)\\Y & = 32.7^(\circ) \; \sf (nearest \: tenth)\end{aligned}`