In right triangle ABC, ∠A is a right angle, m∠B=44∘, and AC=10.
sin44∘≈0.695
cos44∘≈0.719
tan44∘≈0.966
Triangle A B C as described in the text.
What is the measurement of BC?
If necessary, round your answer to one decimal place, like this: 42.5
BC = AC/sin44.
To find the measurement of BC, we can use the trigonometric function cosine (cos) because we know the angle and the length of the adjacent side.
In this case, we have:
cosθ = adjacent/hypotenuse
Here, θ represents angle B and the adjacent side is BC. The hypotenuse is AC, which is given as 10.
So, we can substitute the values:
cos44∘ = BC/10
Now, rearrange the equation to solve for BC:
BC = cos44∘ × 10
Using the approximate value of cos44∘ from the given information (cos44∘≈0.719):
BC ≈ 0.719 × 10 ≈ 7.19
Therefore, the measurement of BC is approximately 7.19 (rounded to one decimal place).
To find the measurement of BC in triangle ABC, we can use trigonometric functions. In this case, we need to use the cosine function.
Given that AC=10 and cos44∘≈0.719, we can use the cosine function to find BC.
cosθ = adjacent/hypotenuse
In this case, θ is the measure of angle B and BC is the adjacent side, so we have:
cos44∘ = BC/AC
Substituting the values we have:
0.719 = BC/10
To find BC, we need to isolate BC on one side of the equation. We can do that by multiplying both sides of the equation by 10:
0.719 * 10 = BC
So, BC ≈ 7.19
Therefore, the measurement of BC is approximately 7.19.