Answer:
segment QS, segment RS
Step-by-step explanation:
Triangle QRS, QS is leg opposite <R and RS is leg adjacent to <R
I would say e and f sorry if wrong
Let ∆ABC is a triangle such that side length of AB is c , BC is a and CA is b .
Given, AB = c = 8
m∠A=60°
m∠C=45°
m∠B = (180 - 45 - 60)° = 75°
use sine rule to get b and c
\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}asinA=bsinB=csinC
so, \frac{sin60^{\circ}}{8}=\frac{sin45^{\circ}}{c}=\frac{sin75^{\circ}}{b}8sin60∘=csin45∘=bsin75∘
sin60°/8 = sin45°/c
(√3/2)/8 = (1/√2)/c
√3/16 = 1/√2c => c = 16/√6
also, sin60°/8 = sin75°/b
b = 8sin75°/sin60°
= {8 × (√3 + 1)/2√2}/{√3/2}
= 4√2(√3 + 1)/√3
hence, perimeter of ∆ABC = a + b + c
= 8 + 16/√6 + 4√2(√3 + 1)/√3
= 8 + (16 + 8√3 + 8)/√6
= 8 + (24 + 8√3)/√6
= 8 + 4√6 + 4√2
area of ∆ABC = 1/2 absinC
= 1/2 × 8 × 4√2(√3 + 1)/√3 × sin45°
= 4 × 4√2(√3 + 1)/√3 × 1/√2
= 16(√3 + 1)/√3
= (48 + 16√3)/3
= 16 + 16/√3
Hi, this is a very easy question :). All you have to do is grab a calculator, and input tangent 27 to it. It would give you the complete answer of 0.5095254495. Rounding off to four decimals, the final answer would be 0.5095. Thus, the answer is letter D.