Find the value of x to the nearest tenth.
hypotenuse: 16
right (90-degree) angle: 72°
show work.
please answer
In a right triangle, the hypotenuse is always opposite to the largest angle, which in this case is 90 degrees. Therefore, the other acute angle in the triangle would be 180 - 90 - 72 = 18 degrees.
Using sine law, we can set up the following equation:
sin 72 / 16 = sin 18 / x
Cross-multiplying and solving for x, we get:
x = 16 * sin 18 / sin 72
Plugging this into a calculator, we get x ≈ 4.6 (rounded to the nearest tenth). Therefore, the value of x to the nearest tenth is 4.6.
Why is the bot using the Sine Law for a right-angled triangle ?????
(and to top it, it matched the hypotenuse of 16 with a non-right-angle !!!! )
It also did not say, what side we want to find
Assuming the base angle is 72°
then
cos72 = x/16
x = 16cos72 = 4.94
sin72 = y/16
y = 16sin72 = 15.2
after you decide what you are supposed to find, pick the appropriate answer.
To find the value of x, we can use the cosine function in a right triangle. The formula for cosine is cos(angle) = adjacent/hypotenuse.
In this case, the angle is 72° and the hypotenuse is 16. So we have:
cos(72°) = x/16
To solve for x, we can rearrange the equation to isolate x:
x = 16 * cos(72°)
Using a calculator or trigonometric table, we can find the cosine of 72°, which is approximately 0.309.
x = 16 * 0.309
x ≈ 4.944
Therefore, the value of x, rounded to the nearest tenth, is approximately 4.9.
To find the value of x, we can use the sine function in trigonometry. The sine function relates the length of the side opposite an angle (in this case, x) to the length of the hypotenuse.
The formula for the sine function is:
sin(angle) = opposite / hypotenuse
We are given the hypotenuse as 16 and the angle as 72°. Plugging in the known values, we can rearrange the formula to solve for x:
sin(72°) = x / 16
Next, we need to solve for x. We can do this by multiplying both sides of the equation by 16:
16 * sin(72°) = x
Using a calculator, we can find the value of sin(72°) to be approximately 0.951.
Calculating further:
16 * 0.951 ≈ 15.216
Therefore, x is approximately 15.216 when rounded to the nearest tenth.