Answer:
Step-by-step explanation:
(a) Radius of circle
The radius r of the circle is AB.
The coordinates of its ends are (5, 10) and (-3, 6).
x = x₂ - x₁ = 5- (-3) = 5 + 3 = 8
y = y₂ - y₁ = 10 - 6 = 4
We can use the Pythagorean theorem to calculate its length.
r² = 8² + 4² = 64 + 16 = 80
r = √80 = 4√5
(b) Slope of line l
Slope of AB = 4/8 = ½
Line l⟂AB, so its slope is the negative reciprocal of the slope of AB .
m = -1/½ = -2
The radius of the circle is and the slope of line l is
.
Answer:
AB = 13.89
Measure of angle A = 59.74°
Measure of angle B = 30.26°
Step-by-step explanation:
The given parameters are;
∠C = 90°
AC = 7
BC = 12
Part 1
Hence, the question has the dimensions of the two adjacent sides of the right angle (angle 90°)
From Pythagoras theorem, we have;
A² = B² + C²
Where, A is the opposite side to the right angle, hence;
In the ΔABC,
AB ≡ A
Therefore;
AB² = AC² + BC² = 7² + 12² = 193
∴ AB = √193 = 13.89
Part 2
∠A is the side opposite side BC such that by trigonometric ratios
∴ ∠A = Arctan(1.714) or tan⁻¹(1.714) = 59.74°
Part 3
∠B is found from knowing that the sum of the angles in a triangle = 180°
∴ ∠A + ∠B + ∠C = 180° which gives
59.74° + 90° + ∠B = 180°
Hence, ∠B = 180° - (59.74° + 90°) = 180° - 149.74° = 30.26°.