Question

what is m∠a? you may round your answer to one decimal place.

b
7
7√2
c
7
a

enter deg after any value that is in degrees.

Explanation:

Step1: Identify triangle type

Triangle \(ABC\) is right - angled at \(C\), with \(AC = 7\), \(BC=7\), and hypotenuse \(AB = 7\sqrt{2}\). Since \(AC = BC = 7\), it is an isosceles right - triangle.

Step2: Calculate angle \(A\)

In an isosceles right - triangle, the two non - right angles are equal. The sum of angles in a triangle is \(180^{\circ}\), and \(\angle C=90^{\circ}\). Let \(\angle A=\angle B = x\). Then \(x + x+90^{\circ}=180^{\circ}\), \(2x = 90^{\circ}\), \(x = 45.0^{\circ}\). We can also use trigonometric ratios. \(\tan(A)=\frac{BC}{AC}=\frac{7}{7} = 1\). Then \(A=\arctan(1)=45.0^{\circ}\) (since \(\tan(45^{\circ}) = 1\)).

Answer:

\(45.0\) deg