Please answer b)only
a) If a triangle has angles of 35 and 65 degrees, what is the measurment of the third angle? Is it a right triangle?
b)Find all angles of a right triangle triangle RST given that r = 18 cm and s = 20 cm
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yes, the sum of angles is 180 in triangle.
b. you know the third side (PYTH theorm). You can find angles from sin, cosine.
To find all the angles of a right triangle RST, we can use the Pythagorean Theorem. According to the Pythagorean Theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In triangle RST, we are given that r = 18 cm and s = 20 cm. Let's use these values to find the missing side, t (the hypotenuse).
Using the Pythagorean Theorem, we have:
t^2 = r^2 + s^2
t^2 = 18^2 + 20^2
t^2 = 324 + 400
t^2 = 724
Now, to find t, we need to take the square root of both sides:
t = √724
t ≈ 26.94 cm
So, the length of the hypotenuse, t, is approximately 26.94 cm.
Now, knowing the lengths of the sides of triangle RST, we can find the angles. To calculate the angles, we can use the following trigonometric ratios:
sinθ = opposite/hypotenuse
cosθ = adjacent/hypotenuse
tanθ = opposite/adjacent
Let's calculate the angles of triangle RST:
Angle R:
sin(R) = opposite (r) / hypotenuse (t)
sin(R) = 18/26.94
R ≈ sin^(-1)(18/26.94)
Angle S:
sin(S) = opposite (s) / hypotenuse (t)
sin(S) = 20/26.94
S ≈ sin^(-1)(20/26.94)
Angle T:
Since triangle RST is a right triangle, we know that the sum of the angles in a triangle is 180 degrees and one angle is 90 degrees (the right angle). Therefore, T = 90 degrees.
So, the angles of triangle RST are approximately R, S, and 90 degrees.