Question

Taina, Luther, and Della are tapping a balloon to each other in the air, trying to keep it from touching the ground. The distance from Taina to Luther is 22 inches. The distance from Luther to Della is 40 inches. The distance from Della to Taina is 34 inches. Find the measures of the three angles in the triangle. Select one: a. m∠L=58.1m∠L=58.1, m∠T=88.5m∠T=88.5, m∠D=33.4m∠D=33.4 b. m∠L=33.4m∠L=33.4, m∠T=58.1m∠T=58.1, m∠D=88.5m∠D=88.5 c. m∠L=88.5m∠L=88.5, m∠T=33.4m∠T=33.4, m∠D=58.1m∠D=58.1 d. m∠L=60m∠L=60, m∠T=60m∠T=60, m∠D=60

Answer 1

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,

$DL^2 = TD^2 + TL^2 - 2\times TD\times TL cos T$

$2\times TD\times TL cos T= TD^2 + TL^2-DL^2$

$\implies cos T = \frac{TD^2 + TL^2-DL^2}{2\times TD\times TL}$

By substituting values,

$cos T = \frac{ 34^2+22^2-40^2}{2\times 34\times 22}$

$cos T = \frac{1156+484-1600}{1496}$

$cos T=\frac{40}{1496}$

$\implies m\angle T=cos^{-1}(\frac{40}{1496})=88.4678446876\approx 88.5^{\circ}$

Similarly,

$cos L = \frac{DL^2 + TL^2-TD^2}{2\times DL\times TL}$

$cos L=\frac{40^2+22^2-34^2}{2\times 40\times 22}$

$cosL=\frac{928}{1760}$

$m\angle L=cos^{-1}(\frac{928}{1760})=58.1786314749\approx 58.1^{\circ}$

$cos D = \frac{DL^2 + TD^2-TL^2}{2\times DL\times TD}$

$cos D=\frac{40^2+34^2-22^2}{2\times 40\times 34}$

$cosD=\frac{2272}{2720}$

$m\angle D=cos^{-1}(\frac{2272}{2720})=33.3535238375\approx 33.4^{\circ}$

Hence, option 'a' is correct.

Answer 2

a. m∠L=58.1m∠L=58.1, m∠T=88.5m∠T=88.5, m∠D=33.4m∠D=33.4