In a right triangle of height 8 cm and base-length 6 cm, what is the measure of

Question

In a right triangle of height 8 cm and base-length 6 cm, what is the measure of the acute angle adjacent to the base? What is the length of hypotenuse ? (use a ruler and a protractor (or this problem) For the above triangle how do you express the ratio between the base and hypotenuse using concepts of trigonometry? What is the acute angle you obtain from this ratio (use a trig table)? Does this angle match with the one you measured in prob.#11? How do you express the height of a right triangle as a function of hypotenuse?

Explanation / Answer

11)

height , h = 8 cm = 0.08 m

base length = 6 cm

for the hypotenuse

length of hypotenuse = sqrt(0.08^2 + 0.06^2)

length of hypotenuse = 0.10 m = 10 cm

for the angle adjacant to base

cos(theta) = 6/10 = 0.60

theta = 53 degree

the angle is 53 degree

12)

for the base to hypotenuse

cos(theta) is used

from this ratio

cos(theta) = 6/10 = 0.60

theta = 53 degree

the angle is 53 degree

yes this mathces.

13)

for the height

sin(theta) is used

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