<em>Question # 1 (Top Left)</em>
<em>Step-by-step Explanation:</em>
<em>To determine:</em>
We have to determine the missing side x.
<em>Given:</em>
- Given angle = 29°
- Right angle = 90°
The missing side x can be calculated by the formula:
sinФ = opposite ÷ hypotenuse
sin(29°) = x ÷ 3
0.4848 = x ÷ 3
x ÷ 3 = 0.4848
x = 0.4848 × 3
x = 1.45 cm
Hence, x = 1.45 cm is the length of missing side.
<em> Question # 2 (Top Center)</em>
<em>Step-by-step Explanation:</em>
<em>To determine:</em>
We have to determine the missing side x.
<em>Given:</em>
- Given angle = 21°
- Right angle = 90°
The missing side x can be calculated by the formula:
tanФ = opposite ÷ adjacent
tan(21°) = x ÷ 4
0.3838 = x ÷ 4
x ÷ 4 = 0.3838
x = 0.3838 × 3
x = 1.15 cm
Hence, x = 1.15 cm is the length of missing side.
<em> Question # 3 (Top Right)</em>
<em>Step-by-step Explanation:</em>
<em>To determine:</em>
We have to determine the missing side x.
<em>Given:</em>
- Given angle = 66°
- Right angle = 90°
The missing side x can be calculated by the formula:
cosФ = adjacent ÷ hypotenuse
cos(66°) = x ÷ 8
0.4067 = x ÷ 8
x ÷ 8 = 0.4067
x = 0.4067 × 8
x = 3.25 cm
Hence, x = 3.25 cm is the length of missing side.
<em> Question # 4 (Bottom Right)</em>
<em>Step-by-step Explanation:</em>
<em>To determine:</em>
We have to determine the missing side x.
<em>Given:</em>
- Given angle = 29°
- Right angle = 90°
The missing side x can be calculated by the formula:
cosФ = adjacent ÷ hypotenuse
cos(29°) = 3.7 ÷ x
0.8746 = 3.7 ÷ x
x = 3.7 ÷ 0.8746
x = 4.23 cm
Hence, x = 4.23 cm is the length of missing side.
<em>Question # 5 (Bottom Center)</em>
<em>Step-by-step Explanation:</em>
<em>To determine:</em>
We have to determine the missing side x.
<em>Given:</em>
- Given angle = 37°
- Right angle = 90°
The missing side x can be calculated by the formula:
sinФ = opposite ÷ hypotenuse
sin(37°) = 5.1 ÷ x
0.6018 = 5.1 ÷ x
x = 5.1 ÷ 0.6018
x = 8.47 cm
Hence, x = 8.47 cm is the length of missing side.
<em> Question # 6 (Bottom Right)</em>
<em>Step-by-step Explanation:</em>
<em>To determine:</em>
We have to determine the missing side x.
<em>Given:</em>
- Given angle = 54°
- Right angle = 90°
The missing side x can be calculated by the formula:
tanФ = opposite ÷ adjacent
tan(54°) = x ÷ 5.9
1.3763 = x ÷ 5.9
x ÷ 5.9 = 1.3763
x = 1.3763 × 5.9
x = 8.12 cm
Hence, x = 8.12 cm is the length of missing side.
<em>Keywords: missing angle, tanФ, cosФ, sinФ, hypotenuse</em>
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