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
Answer:
see explanation
Step-by-step explanation:
Since K is at the midpoint of HN then HK = KN = 4x + 5, thus
HN = HK + KN ← substitute values
11x - 11 = 4x + 5 + 4x + 5, that is
11x - 11 = 8x + 10 ( subtract 8x from both sides )
3x - 11 = 10 ( add 11 to both sides )
3x = 21 ( divide both sides by 3 )
x = 7
Hence
KN = 4x + 5 = (4 × 7) + 5 = 28 + 5 = 33
B. sometimes
sometimes it’s a line and sometimes it’s dashed depending on the less than great than sign
