The answer is A because it is
Answer: 120
Step-by-step explanation:
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.
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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
<span>Simplifying
(5b + -9) + -3(8 + -2b) = 0
Reorder the terms:
(-9 + 5b) + -3(8 + -2b) = 0
Remove parenthesis around (-9 + 5b)
-9 + 5b + -3(8 + -2b) = 0
-9 + 5b + (8 * -3 + -2b * -3) = 0
-9 + 5b + (-24 + 6b) = 0
Reorder the terms:
-9 + -24 + 5b + 6b = 0
Combine like terms: -9 + -24 = -33
-33 + 5b + 6b = 0
Combine like terms: 5b + 6b = 11b
-33 + 11b = 0
Solving
-33 + 11b = 0
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '33' to each side of the equation.
-33 + 33 + 11b = 0 + 33
Combine like terms: -33 + 33 = 0
0 + 11b = 0 + 33
11b = 0 + 33
Combine like terms: 0 + 33 = 33
11b = 33</span>
