Solution:
<u>Note that:</u>
- Slope = m = 4
- Given point: (x₁,y₁) = (1,1) [x₁ = 1; y₁ = 1]
- Formula: y - y₁ = m(x - x₁)
<u>Use the formula to convert the line in point slope form.</u>
- y - y₁ = m(x - x₁)
- y - 1 = 4(x - 1)
The equation of the line (In point slope form) is y - 1 = 4(x - 1).
What we know so far:
Side 1 = 55m
Side 2 = 65m
Angle 1 = 40°
Angle 2 = 30°
What we are looking for:
Toby's Angle = ?
The distance x = ?
We need to look for Toby's angle so that we can solve for the distance x by assuming that the whole figure is a SAS (Side Angle Side) triangle.
Solving for Toby's Angle:
We know for a fact that the sum of all the angles of a triangle is 180°; therefore,
180° - (Side 1 + Side 2) = Toby's Angle
Toby's Angle = 180° - (40° + 30°)
Toby's Angle = 110°
Since we already have Toby's angle, we can now solve for the distance x by using the law of cosines r² = p²+ q²<span>− 2pq cos R where r is x, p is Side1, q is Side2, and R is Toby's Angle.
</span>
x² = Side1² + Side2² - 2[(Side1)(Side2)] cos(Toby's Angle)
x² = 55² + 65² - 2[(55)(65)] cos(110°)
x² = 3025 + 4225 -7150[cos(110°)]
x² = 7250 - 2445.44
x = √4804.56
x = 69.31m
∴The distance, x, between two landmarks is 69.31m
Howwwww.....................
5/7 +1/3
find the common denominator for both of the fractions
common denominator is 21
mutiply by 3 for 5/7
(5)(3)/(7/(3)= 15/21
mutiply by 7 for 1/3
(1)(7)/(3)(7)= 7/21
15/21+7/21
add the numerators
15+7= 22
denominator stays the same -21
Answer:
22/21 or 1 1/21
