In triangle ABC <C=90 degrees, AB=12m and AC=8m. Calculate the measure of <ABC.
so first i recommend drawing a picture. 12 ends up being the hypotenuse and <ABC is across from the leg AC which is 8 so then you use trig to solve
sin(x) = 8/12
x = sin^-1 (aka sin inverse) of 8/12
x is approx. 41.81 degrees
thank you!
To calculate the measure of angle ABC in a right triangle, we can use trigonometric functions. In this case, we will use the sine function.
Step 1: Draw the triangle and label the given side lengths.
Let's draw a triangle ABC where angle C is 90 degrees. Label side AB as 12m and side AC as 8m.
A
|\
| \
8m | \ 12m
| \
---------
B
Step 2: Use the sine function to calculate the angle.
The sine function is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.
sin(angle) = opposite/hypotenuse
In this case, the opposite side to angle ABC is side BC and the hypotenuse is side AB.
sin(ABC) = BC/AB
Step 3: Substitute the given side lengths into the equation.
sin(ABC) = BC/12
Step 4: Solve for BC.
Multiply both sides of the equation by 12:
12 * sin(ABC) = BC
Step 5: Use a calculator to find the value of sin(ABC).
sin(ABC) = 8/12 (opposite/hypotenuse)
sin(ABC) = 2/3
Step 6: Calculate the arc sine (inverse sine) of 2/3 using a calculator.
sin^(-1)(2/3) ≈ 41.81 degrees
Therefore, the measure of angle ABC is approximately 41.81 degrees.