Angles are 18° and 72°
Step-by-step explanation:
- Step 1: Find the two complementary angles in the ratio 1:4. Let the angles be 1x and 4x.
x + 4x = 90° (∵ they are complementary)
5x = 90
∴ x = 90/5 = 18
⇒ Angles are 18° and 4x = 72°
P = ( 2 / 3 )s;
s = ( 3 / 5 )t ;
p + s + t = 280 ;
Then, p =( 2 / 3 )( 3 / 5 )t ;
p = ( 2 / 5 )t;
We solve the equation : ( 2 / 5 )t + ( 3 / 5 )t + t = 280 ;
( 2 / 5 )t + ( 3 / 5 )t + ( 5 / 5 )t = ( 1400 / 5 )t;
10t = 1400 ;
t = 1400 ÷ 10 ;
t = 140 postcards has Tim;
p = ( 2 / 5 ) × 140 = 56 postcards has Paul;
s = ( 3 / 5 ) × 140 = 84 postcards has Shawn ;
Answer:
Step-by-step explanation:
The ladder is the hypotenuse of the triangle with legs of 3 m and 10 m.
<u>The length of the ladder is:</u>
The area of the shape given is 188 mm².
Answer:
1. θ = 34.85°
2. x = 36.31°
3. x = 39.80°
Step-by-step explanation:
1. Determination of θ.
Adjacent = 11.9
Hypothenus = 14.5
Angle θ =?
Cos θ = Adjacent /Hypothenus
Cos θ = 11.9 / 14.5
Cos θ = 0.8207
Take the inverse of Cos
θ = Cos¯¹ 0.8207
θ = 34.85°
2. Determination of x
Opposite = 9 m
Hypothenus = 15.2 m
Angle x =?
Sine x = Opposite /Hypothenus
Sine x = 9 / 15.2
Sine x = 0.5921
Take the inverse of Sine
x = Sine¯¹ 0.5921
x = 36.31°
3. Determination of x
Opposite = 10 in
Adjacent = 12 in
Angle x =?
Tan x = Opposite / Adjacent
Tan x = 10 / 12
Tan x = 0.8333
Take the inverse of Tan
x = Tan¯¹ 0.8333
x = 39.80°
