Answer:
tan (C) = 2.05
Step-by-step explanation:
Given:
A right angled triangle CDE right angled at ∠D.
Side CD = 39
Side DE = 80
Side CE = 89
We know, from trigonometric ratios that, the tangent of any angle is equal to the ratio of the opposite side to the angle and the adjacent side of the angle.
Therefore, tangent of angle C is given as:
Plug in the given values and solve for angle C.This gives,
Therefore, the measure of tangent of angle C is 2.05.
Answer:
1). System of equations- D + Q = 90 and D + 2.5Q = 175.50
2). There are 33 dimes and 57 quarters in the bank.
Step-by-step explanation:
Dylan has a bank that sorts coins as they are dropped in it.
A panel shows the total number of coins inside as well as the total value of these coins.
Let the number of dimes in the bank = D
and the number of quarters in the bank = Q
If the panel shows total number of coins = 90
Then the equation will be
D + Q = 90 -------(1)
And the panel displays the amount of the coins = $17.55
Then equation will be
0.10D + 0.25Q = 17.55 [1 Dime = $0.10 and 1 quarter = $0.25]
D + 2.5Q = 175.50 ------------(2)
Now we subtract equation (1) form equation (2)
D + 2.5Q - (D + Q) = 175.50 - 90
D + 2.5Q - D - Q = 85.5
1.5Q = 85.5
Q =
= 57
By putting Q = 57 in the equation (1)
D + 57 = 90
D = 90 - 57 = 33
Therefore, there are 33 dimes and 57 quarters in the bank.
