Question

In triangle fgh, the measure of angle h is 90°, hg = 33, gf = 65, and fh = 56. What is the value of the tangent of angle g to the nearest hundredth?

Answer 1

The value of tan(g) is approximately 0.59 when rounded to the nearest hundredth, and it is rounded to 0.6 to match the tenths place precision.

Step-by-step explanation:

The question asks for the tangent of angle g in triangle fgh, where angle h is 90°, hg = 33, gf = 65, and fh = 56.

To find the tangent of angle g (tan(g)), we use the definition of tangent in a right triangle, which is the opposite side divided by the adjacent side.

Here, gf is the hypotenuse, hg is opposite to angle g, and fh is adjacent to angle g.

Thus, tan(g) = hg / fh

= 33 / 56.

= 0.589285714.

When rounded to the nearest hundredth, this is approximately 0.59. To round to the nearest tenths place based on 35.5 g which is in tenths place (least precise), we adjust it to 0.6.