Answer:
Step-by-step explanation:
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To find this other side given an angle and a side, we will use a trigonometric function. The three basic ones are sine, cosine, and tangent. You can remember these and what what they are using the mnemonic "soh cah toa".
SOH: Sine= Opposite/Hypotenuse
CAH: Cosine= Adjacent/Hypotenuse
TOA: Tangent= Opposite/Adjacent
We see that the sides involved are the opposite and hypotenuse.
Therefore, we can write this equation.
sin40= w/28
We multiply both sides by 28 to isolate the w.
28×sin40=w
Now, we find the sine of 40 on our calculator and then we multiply it by 28.
w≈18
Therefore, the answer is 18 cm.
I hope that this helps! Have a wonderful day!
According to Google.com, a rational number is “a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.”
I'll start with the triangle figure.
Interior angles of a triangle is equal to 180°. The given triangle is an Isosceles triangle. It has 2 equal sides and 2 equal angles.
#7 is 69° because its vertical angle is 69°. Vertical angles are equal.
#8 is 111°. As I said, isosceles triangle has 2 equal angles. The angle that is beside #8 is 69°, equal to #7. So, 180° - 69° = 111°
Interior angles are already given except for #4. So, 180° - 69° - 69° = 42°
#3 is computed by 180° - 42° - 69° = 69°
#9 = 116° ; alternate interior angles are equal.
#10 = 180° - 116° = 64°
The last triangle looks like an equilateral triangle. It means that its sides and angles are equal.
360° / 6 = 60°
#1, #2, #5, and #6 = 60° each
#11 = 60° - equilateral triangle, all interior angles are equal.
#12 = 30°; 180° - 90° - 60° = 30°
Let Mary's age be x.
Paul is three times as old as Mary, so Paul's age would be 3x.
Peter is four times as old as Mary, so Peter's age would be 4x.
The sum of their ages is 64
⇒ Paul's age+ Peter's age+ Mary's age= 64
⇒ 3x+ 4x+ x= 64
⇒ 8x= 64
⇒ x= 64/8
⇒ x= 8
Paul's age is: 3x= 3*8= 24
Peter's age is: 4x= 4*8= 32
Final answer: Paul is 24 years old.
Peter is 32 years old.
Mary is 8 years old.
Hope this helps~
