# 4th Sample Math Challenge Questions and Answers III( Trigonometry and Combinatorics )

- What is in degrees?
- Convert 235° to radians.
- Evaluate: sin14°cos16°+cos14°sin16°
- Find the length of an arc subtended by an angle of 60° in a circle if the radius is 5cm.
- Evaluate : sin3150°
- If sinX=2/3 and X is in second quadrant. What is cosX?
- The angle of elevation of an object from the top of the tree is 30°. If the height of the tree is 15m. How far is the object from the tree?
- Twice the supplement of the angle is two more than the compliment of the angle. What is the angle?
- The length of the diagonal of the rectangle is 20 cm. If the diagonal makes an angle of 30° with the longer side. What is the area of rectangle?
- Solve for X in (0,360°): 4cos
^{2}X-1=0. - What is the amplitude and period of the y=2sin3x
- What is the range of y=3+2sinx?
- John walked 20m from point A to B. From B he made a left making an angle of 60 degrees with his previous path, after reaching 25 m he decided to go back to point A. How long will he need to walk again?
- Two sides of triangle measures 6 cm and 10 cm. What is the area of the smallest triangle with integral sides that can be made out of these sides?
- The angle of elevation of the car from the top tower is 30°. The car travelled with a uniform speed of 20 kph, after 20 minutes the angle of elevation of the car from the top of the tower is 45°. What is the height of the tower?
- An equilateral triangle is inscribed in a circle, if the radius of the circle is 10cm. What is the area of the triangle?
- Jane has 8 shirts and 9 pants. How many clothing combinations does Jane have, if she doesn’t wear 2 specific shirts with 3 specific pants?
- Out of a classroom of 6 boys and 4 girls the teacher picks a president for the student board, a vice president and a secretary. What is the probability that only girls will be elected?
- Two dice are rolled. What is the probability the sum will be greater than 10?
- In Manila, the chance for rain on any given day is 40%. What is the probability that it rains on 5 out of 7 consecutive days in Manila?
- In how many ways 4 people can be arrange in a circle?
- How many diagonals does decagon have?
- How many 3-digit numbers can be formed with the digits 1,4,7,8 and 9 if the digits are not repeated.
- How many permutations does the word CHACHA have?
- Given 4 letters and 4 addressed envelopes, in how many ways can the letters be placed in the envelopes so that no letter is in the correct envelope?

### Dan

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