In right triangle ABC, ∠C is a right angle, m∠B=70∘, and AB=13.
sin70∘≈0.94
cos70∘≈0.34
tan70∘≈2.75
What is the measurement of BC?
Well, since we have a right triangle, we can use the Pythagorean theorem. But before that, let me ask you, do you know why triangles are so popular at parties? Because they're always right-angular! Okay, now back to the problem.
Using the Pythagorean theorem, we have:
BC^2 = AB^2 - AC^2
Since AC is the side opposite the right angle, we can use the sine of angle B to find its length:
AC = AB * sin(B)
AC = 13 * sin(70°)
AC ≈ 13 * 0.94
AC ≈ 12.22
Now, plugging the values into the equation:
BC^2 = 13^2 - 12.22^2
BC^2 ≈ 169 - 149.28
BC^2 ≈ 19.72
BC ≈ √19.72
BC ≈ 4.43
So, the measurement of BC is approximately 4.43 units. Keep in mind, I rounded the answer!
To find the length of BC, we can use the trigonometric ratio sine (sin). In a right triangle, the sine of an angle is defined as the length of the side opposite the angle divided by the length of the hypotenuse.
In this case, the side opposite angle B is BC and the hypotenuse is AB. We know that AB is equal to 13.
Using the given approximation, sin70°≈0.94, we can set up the equation:
sin70° = opposite/hypotenuse
0.94 = BC/13
To solve for BC, we can cross multiply:
0.94 × 13 = BC
12.22 ≈ BC
Therefore, the measurement of BC is approximately 12.22.
To find the measurement of BC in right triangle ABC, we can use the trigonometric ratio called "sine" (sin).
In this case, the given information is that ∠B = 70° and AB = 13.
The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we are looking for the length of side BC (opposite the angle ∠B), so we will use the sine ratio.
Using the sine ratio:
sin(∠B) = opposite / hypotenuse
Substituting the known values:
sin(70°) = BC / 13
Now, we can solve for BC by multiplying both sides of the equation by 13:
13 * sin(70°) = BC
Finally, we can use a calculator to find the approximate value of sin(70°) and compute the value of BC:
BC ≈ 13 * 0.94
BC ≈ 12.22
Therefore, the measurement of BC in triangle ABC is approximately 12.22 units.
AB, the hypotenuse, is 13
angle B is 70
cos 70 = BC/13
so
BC = 13 cos 70