Question

sin b =
tan b =
cos b =
(right triangle xyz with x right angle, xz=18.4, xy=34.5, yz=39.1; right triangle abc with a right angle)

Explanation:

Step1: Identify sides for angle B (assuming triangle XYZ is similar or we use triangle ABC with right angle at A, and triangle XYZ has right angle at X. Wait, maybe the triangle with right angle at X: XZ=18.4, XY=34.5, YZ=39.1. Wait, maybe the triangle ABC: right angle at A, so for angle B, opposite side is AC, adjacent is AB, hypotenuse is BC. But maybe the triangle XYZ: right angle at X, so angle at Y? Wait, the labels: X is right angle, so sides: XZ=18.4 (opposite to Y), XY=34.5 (adjacent to Y), YZ=39.1 (hypotenuse). Wait, maybe the problem is about triangle ABC, but the other triangle is a reference. Wait, let's assume the triangle with right angle at A (triangle ABC), and we need to find sin B, tan B, cos B. Wait, maybe the lengths are from triangle XYZ: XZ=18.4, XY=34.5, YZ=39.1. Wait, maybe angle B is in triangle ABC, and the sides correspond. Wait, perhaps the triangle XYZ is a right triangle at X, so sides: XZ=18.4 (leg), XY=34.5 (leg), YZ=39.1 (hypotenuse, since 18.4² +34.5² ≈ 338.56 + 1190.25 = 1528.81, and 39.1²≈1528.81, so yes, right triangle at X. So angle at Y: let's call angle Y as B. Then for angle B (at Y), opposite side is XZ=18.4, adjacent side is XY=34.5, hypotenuse is YZ=39.1.

Step2: Calculate sin B

Sin B = opposite/hypotenuse = 18.4 / 39.1 ≈ 0.4706

Step3: Calculate cos B

Cos B = adjacent/hypotenuse = 34.5 / 39.1 ≈ 0.8824

Step4: Calculate tan B

Tan B = opposite/adjacent = 18.4 / 34.5 ≈ 0.5333

Answer:

sin B ≈ 0.471, tan B ≈ 0.533, cos B ≈ 0.882 (rounded to three decimal places)

Wait, let's recalculate:

Sin B = opposite/hypotenuse = 18.4 / 39.1 ≈ 18.4 ÷ 39.1 ≈ 0.4706 ≈ 0.471

Cos B = 34.5 / 39.1 ≈ 34.5 ÷ 39.1 ≈ 0.88235 ≈ 0.882

Tan B = 18.4 / 34.5 ≈ 18.4 ÷ 34.5 ≈ 0.53333 ≈ 0.533

So:

sin B = 18.4 / 39.1 ≈ 0.471

cos B = 34.5 / 39.1 ≈ 0.882

tan B = 18.4 / 34.5 ≈ 0.533