Question

Find the missing information for the triangle.

Answer 1

missing angle:

180° - 90° - 30°

180° - 120°

60°

missing sides:

(a)

$\rightarrow \sf tan(x)= \dfrac{opposite}{adjacent}$

$\rightarrow \sf tan(30)= \dfrac{4}{adjacent}$

$\rightarrow \sf adjacent= \dfrac{4}{tan(30)}$

$\rightarrow \sf adjacent= 4\sqrt{3}$

$\rightarrow \sf adjacent= 6.93 \ cm$

(b)

$\sf \rightarrow sin(x)= \dfrac{opposite}{hypotensue}$

$\sf \rightarrow sin(30)= \dfrac{4}{hypotensue}$

$\sf \rightarrow hypotensue= \dfrac{4}{ sin(30)}$

$\sf \rightarrow hypotensue= 8 \ cm$

Answer 2

Answer:

m∠X = 60°

BX = 8 cm

BM = 4√3 cm

Step-by-step explanation:

The sum of the interior angles of a triangle is 180°

Given:

• m∠B = 30°
• m∠M = 90°

⇒ m∠B + m∠M + m∠X = 180°

⇒ 30° + 90° + m∠X = 180°

⇒ 120° + m∠X = 180°

⇒  m∠X = 180° - 120°

⇒  m∠X = 60°

Using the sine rule to find the side lengths:

$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

(where A, B and C are the angles, and a, b and c are the sides opposites the angles)

Given:

• m∠X = 60°
• m∠B = 30°
• m∠M = 90°
• MX = 4 cm

$\implies \dfrac{4}{\sin 30\textdegree}=\dfrac{BX}{\sin 90\textdegree}=\dfrac{BM}{\sin 60\textdegree}$

$\implies BX=\sin 90\textdegree \cdot\dfrac{4}{\sin 30\textdegree}$

              $=1 \cdot \dfrac{4}{\frac12}$

              $=1 \cdot 4 \cdot 2$

              $=8 \textsf{ cm}$

$\implies BM=\sin 60\textdegree \cdot\dfrac{4}{\sin 30\textdegree}$

              $=\dfrac{\sqrt{3}}{2}\cdot \dfrac{4}{\frac12}$

              $=\dfrac{\sqrt{3}}{2}\cdot 4 \cdot 2$

              $=4\sqrt{3} \textsf{ cm}$