consider the triangle.
angle a=
angle b = 30°
angle c = 90°
ab = 10
ac = 5
bc=

Question

Accepted Answer

# Explanation:
## Step1: Use the sum of angles in a triangle
The sum of angles in a triangle is $180^{\circ}$. Let $\angle A=x$. Then $x + 30^{\circ}+90^{\circ}=180^{\circ}$.
## Step2: Solve for $\angle A$
$$
\begin{align*}
x&=180^{\circ}-(30^{\circ}+90^{\circ})\
x&=180^{\circ}-120^{\circ}\
x& = 60^{\circ}
\end{align*}
$$
## Step3: Use the Pythagorean theorem for $BC$
In a right - triangle $ABC$ with $AB = 10$, $AC = 5$, and $BC$ as one of the legs. By the Pythagorean theorem $AB^{2}=AC^{2}+BC^{2}$. Let $BC = y$, then $y^{2}=AB^{2}-AC^{2}$.
$$
\begin{align*}
y^{2}&=10^{2}-5^{2}\
y^{2}&=100 - 25\
y^{2}&=75\
y&=\sqrt{75}\
y&=5\sqrt{3}
\end{align*}
$$

# Answer:
Angle $A = 60^{\circ}$, $BC=5\sqrt{3}$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the sum of angles in a triangle

Step2: Solve for \(\angle A\)

Step3: Use the Pythagorean theorem for \(BC\)

Answer: