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
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:
Step-by-step explanation:
Since, angle 1 is an exterior angle of ΔABE,
m∠1 > m∠3 and m∠4
Since, angle 1 is an exterior angle of ΔABD,
m∠1 > m∠5
Since, angle 1 is an exterior angle of ΔABC,
m∠1 > m∠7 and m∠8
Therefore, ∠1 is greater than ∠3, ∠5, ∠7 and ∠8.
Answer:
Step-by-step explanation:
Think of this situation as a number line in which the team starts at 0 yd.
Gaining yards is the positive direction and losing yards is negative.
Start at 0 yd and go 5 yd to the right. You are at +5.
Then go 7 yd left. You end up at -2.
+5 – 7 = -2
