To the nearest degree, what is the measure of the smallest angle of a right triangle whose legs measure 9 and 15?
Tangent= Opposite/Hypotenuse
Tan 9/15=30.96 (This is the Smallest Angle)
Check:
90(This is the Right angle)+30.96=120.9
180-120.9=59.1(This is the third angle.)
9/sin 30.96 = 15/sin 59.1.
This Does Work.
So the Smallest Angle is 30.9 Degrees, rounded to 31.
The answer of 31° is correct.
Your definition of tangent was probably a typo, and it should read:
Tangent = opposite / adjacent
Determine the measure, to the nearest degree, of the smallest angle in a triangle with sides
of 4 m, 7 m, and 8 m. Sketch the triangle.
Well, if we're talking about a right triangle, it's always a "right" decision to use some basic math! The Pythagorean theorem states that in a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse. In this case, we have legs that measure 9 and 15. So, using the theorem, we have 9^2 + 15^2 = c^2, where c is the length of the hypotenuse. Simplifying that, we get 81 + 225 = c^2, which gives us c^2 = 306. Now it's time to square root that number, and we find that c is approximately 17.5.
Since we know a right triangle has a 90-degree angle, and the smallest angle is always opposite the smallest side, we now need to find the smallest angle. We divide the length of the smallest side (9) by the length of the hypotenuse (17.5) and then take the inverse cosine (or the arccos) of that value to find the smallest angle.
After doing some calculations, the smallest angle of this right triangle is approximately 29.5 degrees. So, grab your protractor and enjoy your newfound knowledge!
To find the measure of the smallest angle of a right triangle with legs measuring 9 and 15, we can use trigonometric ratios. In a right triangle, the smallest angle is always opposite the smallest side.
First, calculate the length of the hypotenuse using the Pythagorean theorem:
hypotenuse^2 = leg1^2 + leg2^2
hypotenuse^2 = 9^2 + 15^2
hypotenuse^2 = 81 + 225
hypotenuse^2 = 306
hypotenuse ≈ √306
hypotenuse ≈ 17.5 (rounded to one decimal place)
Next, we can use the sine function to find the measure of the smallest angle. Recall that the sine of an angle is equal to the ratio of the side opposite the angle to the hypotenuse.
sin(smallest angle) = opposite / hypotenuse
sin(smallest angle) = 9 / 17.5
smallest angle ≈ sin^(-1)(9 / 17.5)
smallest angle ≈ 30.6 degrees (rounded to the nearest degree)
Therefore, the measure of the smallest angle in the right triangle is approximately 31 degrees.
There are two acute angles in a right triangle. The tangents of these angles are the ratio of the legs. The small ratio corresponds to the smaller angle.
You'd be looking for tan-19/15.