In right triangle DEF, cosD=12/17. The measure of angle D, to the nearest tenth of a degree, is ______.
cos45.1° ≈ 12/17
To find the measure of angle D in the right triangle DEF, we can use the inverse cosine function, also known as the arccosine function.
The formula is: angle D = arccos (adjacent/hypotenuse)
Given that cosD = 12/17, we can substitute the values into the formula:
angle D = arccos (12/17)
To find the measure of angle D, we need to calculate the arccosine of 12/17. Let's use a calculator or a math software that has the arccosine function.
By evaluating arccos (12/17), we obtain the result approximately equal to 0.8411 radians.
To convert the result to degrees, we multiply by 180/π (where π is approximately 3.14159):
angle D (in degrees) ≈ 0.8411 × (180/π) ≈ 48.4 degrees
Therefore, the measure of angle D in the right triangle DEF, to the nearest tenth of a degree, is approximately 48.4 degrees.
To find the measure of angle D in right triangle DEF, we can use the inverse cosine function (also known as arccosine). The formula for finding the measure of an angle given the cosine value is:
angle = arccos(cosine value)
Substituting the given value, we have:
angle D = arccos(12/17)
Using a calculator to evaluate this, the measure of angle D is approximately 41.8 degrees to the nearest tenth.