Answer:
a. m∠L=58.1, m∠T=88.5, m∠D=33.4
Step-by-step explanation:
Suppose T, L and D represents Taina, Luther, and Della respectively,
According to the question,
TD = 34 inches,
TL = 22 inches,
DL = 40 inches,
By the law of cosine,
[tex]DL^2 = TD^2 + TL^2 - 2\times TD\times TL cos T[/tex]
[tex]2\times TD\times TL cos T= TD^2 + TL^2-DL^2[/tex]
[tex]\implies cos T = \frac{TD^2 + TL^2-DL^2}{2\times TD\times TL}[/tex]
By substituting values,
[tex]cos T = \frac{ 34^2+22^2-40^2}{2\times 34\times 22}[/tex]
[tex]cos T = \frac{1156+484-1600}{1496}[/tex]
[tex]cos T=\frac{40}{1496}[/tex]
[tex]\implies m\angle T=cos^{-1}(\frac{40}{1496})=88.4678446876\approx 88.5^{\circ}[/tex]
Similarly,
[tex]cos L = \frac{DL^2 + TL^2-TD^2}{2\times DL\times TL}[/tex]
[tex]cos L=\frac{40^2+22^2-34^2}{2\times 40\times 22}[/tex]
[tex]cosL=\frac{928}{1760}[/tex]
[tex]m\angle L=cos^{-1}(\frac{928}{1760})=58.1786314749\approx 58.1^{\circ}[/tex]
[tex]cos D = \frac{DL^2 + TD^2-TL^2}{2\times DL\times TD}[/tex]
[tex]cos D=\frac{40^2+34^2-22^2}{2\times 40\times 34}[/tex]
[tex]cosD=\frac{2272}{2720}[/tex]
[tex]m\angle D=cos^{-1}(\frac{2272}{2720})=33.3535238375\approx 33.4^{\circ}[/tex]
Hence, option 'a' is correct.
