In right triangle XYZ, ∠Z is a right angle, m∠Y=16∘, and XZ=7.
sin16∘≈0.276
cos16∘≈0.961
tan16∘≈0.287
Triangle X Y Z as described in the text.
What is the measurement of YZ?
If necessary, round your answer to one decimal place, like this: 42.5
The answer is 24.4
Well, to find the measurement of YZ, we can use the sine function. Since we know that sin(16∘) is approximately 0.276, we can set up the equation sin(16∘) = YZ / XZ. Plugging in the known values, we get 0.276 = YZ / 7. To solve for YZ, we can multiply both sides of the equation by 7, giving us YZ = 7 * 0.276. So, YZ ≈ 1.932. But since we need to round our answer to one decimal place, YZ is approximately 1.9. So, the measurement of YZ is approximately 1.9. It's like YZ went on a diet and got lighter!
To find the measurement of YZ, we can use the trigonometric ratio sine (sin) which relates the lengths of the sides of a right triangle to the angles. In this case, we know the measurement of angle Y which is 16∘ and we know the measurement of angle Z which is 90∘ (because it's a right triangle). Hence, angle X must be (180 - 90 - 16) = 74∘.
Now, we can use the sine ratio:
sin θ = opposite/hypotenuse
In triangle XYZ, YZ is the side opposite to angle XZ, so we have:
sin 74∘ = YZ / 7
To find YZ, we can rearrange the equation as follows:
YZ = sin 74∘ * 7
Using a scientific calculator, we can substitute the value of sin 74∘ which is approximately 0.927 and multiply it by 7:
YZ ≈ 0.927 * 7 ≈ 6.49
Therefore, the measurement of YZ is approximately 6.5 (rounded to one decimal place).