Question

5. Solve the following triangle for all missing sides and angles.

Answer 1

Answer:

$Part I: Measure of angle A=100°$

$Part II: Length of side a using sines law=29.56$

$Part III: Length of side a using sines law=24.21$

Step-by-step explanation:

Given:-

$∠B = 45°$

$∠C = 35°$

$Length of side AB = 17$

Solution:-

1] To find Measure of ∠A=?

Solution:-

$Sum of angle of triangle = 180°$

$i.e. ∠A+∠B+∠C=180°$

$∠A+45+35=180$

$∠A=180-45-35$

$∠A=100°$

2] To find length of side a using sines law

Solution:-

$sines C = \frac{opposite}{hypotenuse}$

$sines C= \frac{length AB}{a}$

$sines C=\frac{17}{side a}$

$side a=\frac{17}{sines C}$

$side a=\frac{17}{0.575}$

$side a=29.56$ ------------------------------ (equation 1)

3] To find length of side b using cosines law

Solution:-

$cosines C=\frac{adjacent}{hypotenuse}$

$cosines C=\frac{lengthAC}{hypotenuse}$

$cosines 35=\frac{b}{29.56}$  ----------------------------(from equation )

$b=cosines 35\ times 29.56$

$b=0.819\times 29.56$

$b=24.21$

Answer 2

Answer:

Part I : 100°

Part II : a = 29.2

Part III : b = 20.95

Step-by-step explanation:

See the attached diagram of the triangle.

Part I: ∠ A = 180° - ∠ B - ∠ C = 180° - 45° - 35° = 100°

Part II: Now, applying the law of sines, we have

$\frac{AB}{\sin 35^\circ} = \frac{BC}{\sin 100^\circ}$

⇒ $\frac{17}{\sin 35^\circ} = \frac{a}{\sin 100^\circ}$

⇒ $a = \frac{17}{\sin 35^\circ} \times \sin 100^\circ$

⇒ a = 29.2 (Answer)

Part III: Now, applying law of cosine, we have  

b = a cos 35° + c cos 100° = 29.2 cos 35° + 17 cos 100° = 20.95 (Answer)