Answer:
24.315°
Step-by-step explanation:
First use the pythagorean theorem to get the missing side since this is a right triangle.
a^2 + b^2 = c^2 →
b^2 = c^2 – a^2 →
b = (c^2 – a^2)^½
b = (17^2 – 7^2)^½
b = (289 – 49)^½
b = √240.
Then use the law of cosines to find the angle in between.
b^2 = a^2 + c^2 - 2ac * cos(B) →
b^2 - a^2 - c^2 = -2ac * cos(B) →
a^2 + c^2 – b^2 / 2ac = cos(B) →
cos^-1(a^2 + c ^2 – b^2 / 2ac) = C →
B = cos^-1(a^2 + c ^2 – b^2 / 2ac)
B = cos^-1(49 + 289 – √240 / 238)
B ≈ 75.685°.
A = 180 – B
A = 180 – 75.685
A = 24.315°
