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G-SRT.6 Warmup M2-051-A06-V04

Define trigonometric ratios for acute angles using right-triangle similarity.

Compute separate sine, cosine, and tangent fields

Problem

The similar \(7-24-25\) and \(14-48-50\) right triangles share reference angle \(θ\), with opposite, adjacent, and hypotenuse corresponding in that order. Calculate \(\sin(θ)\), \(\cos(θ)\), and \(\tan(θ)\), then verify that scaling leaves each ratio unchanged.

Prompt diagram of similar right triangles with the same reference angle theta. In the smaller triangle, opposite = 7, adjacent = 24, hypotenuse = 25; in the scale-factor-2 triangle, the corresponding sides are 14, 48, and 50. The trig ratios are withheld. Open full size
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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-SRT.6
Category
Geometry
Domain
Similarity, Right Triangles, and Trigonometry
Objective
Define trigonometric ratios for acute angles using right-triangle similarity.
Problem type
Compute separate sine, cosine, and tangent fields