The legs of a right triangle measures 3 and 4. Find to the nearest degree the measure of the smallest angle of this triangle.
Please show me how to do this
2007-09-11 10:45:31 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Given that this is a right triangle, the smallest angle, theta, is given by the formula:
tan(theta)= opposite side divided by the adjacent side = 3/4
Therefore,
theta = arctan(3/4)=36.87degrees = 37 degrees.
Note that arctan is the inverse function of the tangent; the angle that has a tangent equal to a given number, 3/4 in this case.
You could get the same result, using other trig functions. You know that the hypotenuse in a 3-4 right triangle is 5 (3-4-5) triangle.
So:
sin(theta)= opposite side divided by hypotenuse = 3/5 -->
theta = arcsin(3/5) = 36.87 degrees = 37 degrees, and
cos(theta)= adjacent side divided by hypotenuse = 4/5 -->
theta = arccos(4/5) = 36.87 degrees = 37 degrees
2007-09-11 11:00:15 · answer #1 · answered by Anthony P - Greece 2 · 0⤊ 0⤋
The smallest angle is across from the smallest side.
Pick some variable (usually theta for angles) and label the side across from the side of length 3 with this variable.
Use the definitions of trig functions to make an equation with your variable and the lengths given.
2007-09-11 10:52:51 · answer #2 · answered by Demiurge42 7 · 0⤊ 0⤋
TAN (X) = 4/3
X = invtan (3/4)
2007-09-11 10:50:11 · answer #3 · answered by Jeffrey K 7 · 0⤊ 1⤋
Well, I think there must be some other information...
2007-09-11 10:51:09 · answer #4 · answered by Anonymous · 0⤊ 1⤋