Based on my analysis of the worksheet, I can solve the trigonometry problems presented.
The worksheet contains several problems related to finding trigonometric ratios (sine, cosine, and tangent) in right triangles.
Problem 1: Triangle with sides 5, 12, 13
This is a right triangle where:
- Opposite side to angle θ = 5
- Adjacent side to angle θ = 12
- Hypotenuse = 13
Using the definitions of trigonometric ratios:
- sin θ = opposite/hypotenuse = 5/13
- cos θ = adjacent/hypotenuse = 12/13
- tan θ = opposite/adjacent = 5/12
Problem 2: Triangle with sides 6, 8, 10
This is another right triangle (a 3-4-5 triangle scaled by 2) where:
- If we consider the angle opposite the side of length 6, then:
- Opposite = 6
- Adjacent = 8
- Hypotenuse = 10
- sin θ = 6/10 = 3/5
- cos θ = 8/10 = 4/5
- tan θ = 6/8 = 3/4
- If we consider the angle opposite the side of length 8, then:
- Opposite = 8
- Adjacent = 6
- Hypotenuse = 10
- sin θ = 8/10 = 4/5
- cos θ = 6/10 = 3/5
- tan θ = 8/6 = 4/3
The worksheet appears to be teaching students how to calculate trigonometric ratios using the sides of right triangles. The key is to identify which side is opposite, which is adjacent, and which is the hypotenuse relative to the angle in question, then apply the appropriate ratio formula.
The solutions involve simple fraction calculations based on the side lengths provided in each triangle diagram.
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