Solve each triangle. Round your answers to the nearest tenth. m∠A = 60°, m∠B = 30°, c = 30 cm
2 answers:
Answer:
Angle C = 90°
a = 15sqroot3
b = 15
Step-by-step explanation:
Solve a triangle means to find all the angles and all the sides.
Angle C must be 90° because all the angles of a triangle add up to 180°.
That makes this a 30°-60°-90° triangle so there are SHORTCUTS to finding the sides so you don't have to use trig or pythagorean thm.
SHORTCUT:
The shortest side is half the longest side. (The short leg is half the hypotenuse) and/or the longest side is twice the shortest side.
SHORTCUT:
The long leg is the shortleg•sqroot3
(advanced mode: the shortleg is the longleg/sqrt3)
So for your problem, the hypotenuse is 30, so the short leg is 15. And that makes the long leg 15sqrt3. See image.
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The value of x is 11.
Solution:
JH is a midsegment of the triangle KLM.
LM = 22
JH = x
To find the value of x.
<u>Mid-segment theorem:</u>
<em>The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half the length of the third side.</em>
By the mid-segment theorem,
JH = Half of LM
x = 11
The value of x is 11.