Question

100 points !! 3 answers !!

Instructions: Find the missing side. Round your answer to the nearest tenth.

Answer 1

#1

• cos28=x/25
• x=25cos28
• x=22.1

#2

• cos26=x/15
• x=15cos26
• x=16.7

#3

• tan41=x/16
• x=16tan41
• x=14

Answer 2

Trigonometric ratios

`\sf \sin(\theta)=(O)/(H)\quad\cos(\theta)=(A)/(H)\quad\tan(\theta)=(O)/(A)`

where:

• 
  `\theta` is the angle
• O is the side opposite the angle
• A is the side adjacent the angle
• H is the hypotenuse

Given:

• 
  `\theta` = 28°
• A = x
• H = 25

`\implies \sf \cos(28^(\circ))=(x)/(25)`

`\implies \sf x=25cos(28^(\circ))`

`\implies \sf x=22.1\:(nearest\:tenth)`

Given:

• 
  `\theta` = 26°
• A = 15
• H = x

`\implies \sf \cos(26^(\circ))=(15)/(x)`

`\implies \sf x=(15)/(\cos(26^(\circ)))`

`\implies \sf x=16.7\:(nearest\:tenth)`

Given:

• 
  `\theta` = 41°
• O = x
• A = 16

`\implies \sf \tan(41^(\circ))=(x)/(16)`

`\implies \sf x=16\tan(41^(\circ))`

`\implies \sf x=13.9\:(nearest\:tenth)`