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(8) Angle S is 90 degrees and angle T is 45 degrees. Side ST is 3 feet. How long is side SU ?

(88) Angle S S is 9090 degrees and angle T T is 4545 degrees. Side ST S T is 33 feet. How long is side SU S U ?

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Full solution

Q. (88) Angle S S is 9090 degrees and angle T T is 4545 degrees. Side ST S T is 33 feet. How long is side SU S U ?
  1. Identify Triangle Type: Since angle SS is 9090 degrees, angle TT is 4545 degrees, and STST is 33 feet, triangle STUSTU is a right-angled isosceles triangle (because the angles are 4545, 4545, and 9090 degrees).
  2. Apply Property of Right-Angled Isosceles Triangle: In a right-angled isosceles triangle, the lengths of the two legs are equal. So, side STST is equal to side SUSU.
  3. Determine Length of Side SU: Therefore, the length of side SU is also 33 feet.

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