Let the speed of the current equal c
and the speed of the boat in still water equal b.
b + c = 1.5 (b - c)
b + c = 1.5b - 1.5c
0.5b = 2.5c
b = 5c
The speed of the current is 1.5 mph so
b = 5 * 1.5 = 7.5 mph
Answer:
- angle at A: 51°
- base angles: 64.5°
Step-by-step explanation:
The measure of the inscribed angle BAC is half the measure of the intercepted arc BC, so is 102°/2 = 51°.
The base angles at B and C are the complement of half this value, or ...
90° -(51°/2) = 64.5°
The angle measures in the triangle are ...
∠A = 51°
∠B = ∠C = 64.5°
We are given: cos theta = 1/3. Thus, adj side = 1 and hyp = 3. Using the Pythagorean Theorem to find the length of the opposite side, represented by x.
1^2 + opp^2 = 3^2, or 1 + x^2 = 9, or x^2 = 8. Here, x could be either sqrt(8) or -sqrt(8): sqrt(8) if angle theta is in QI, and -sqrt(8) if in QIV.
Thus, the sine of angle theta could be either sqrt(8)/3 or -sqrt(8)/3.
