One angle of a triangle is 55 ° and the second angle is π 12 , find the third angle in circular measure.

Given that: One angle of a triangle is 55 ° and the second angle is π 12 , Let the third angle in circular measure be x radian Now we know that, 180 ° = π radian 1 ° = π 180 radian Then, 55 ° = π 180 × 55 radian 55 ° = 11 π 36 radian Now, by angle sum property of triangle, 11 π 36 + π 12 + x = π x = π - 11 π 36 - π 12 x = 36 π - 11 π - 3 π 36 x = 22 π 36 = 11 π 18 radian Therefore, the third angle in circular measure is 11 π 18 .

One angle of a triangle is 55 ° and the second angle is π 12 , find the third angle in circular measure.

Given that: One angle of a triangle is 55 ° and the second angle is π 12 , Let the third angle in circular measure be x radian Now we know that, 180 ° = π radian 1 ° = π 180 radian Then, 55 ° = π 180 × 55 radian 55 ° = 11 π 36 radian Now, by angle sum property of triangle, 11 π 36 + π 12 + x = π x = π - 11 π 36 - π 12 x = 36 π - 11 π - 3 π 36 x = 22 π 36 = 11 π 18 radian Therefore, the third angle in circular measure is 11 π 18 .

Solve: x - 3 x + 3 + x + 3 x - 3 = 2 1 2

We have, x - 3 x + 3 + x + 3 x - 3 = 2 1 2 ⇒ x - 3 2 + x + 3 2 x + 3 x - 3 = 5 2 ⇒ x 2 + 9 - 6 x + x 2 + 9 + 6 x x 2 - 3 2 = 5 2 [using a + b 2 = a 2 + b 2 + 2 a b , a - b 2 = a 2 + b 2 - 2 a b and a + b a - b = a 2 - b 2 ] ⇒ 2 x 2 + 18 x 2 - 9 = 5 2 ⇒ 2 2 x 2 + 18 = 5 x 2 - 9 ⇒ 4 x 2 + 36 = 5 x 2 - 45 x 2 - 81 = 0 x + 9 x - 9 = 0 x = 9 and x = - 9 Therefore, the value of x = ± 9 .

E M B I B E

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 4

MEDIUM

10th West Bengal Board

IMPORTANT

Earn 100

One angle of a triangle is $55 °$ and the second angle is $\frac{π}{12}$ , find the third angle in circular measure.

Important Questions on Third Summative Test

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 4

The height of a right circular cylinder is equal to its diameter. If the whole surface area of the cylinder is equal to its volume, what is the diameter of the cylinder ?

EASY

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 4

Find the volume of a maximum sphere which can be placed in a cubical can box of side

6 c m

.

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 4

Find the mean from the following frequency distribution table :

Number	$5$	$10$	$15$	$20$	$25$	$30$	$35$
Frequency	$1$	$2$	$5$	$6$	$3$	$2$	$1$

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 5

The price of an instrument decreases at the rate of $12.5 %$ every year. What will be the percentage of decrease of the instrument after $2$ years?

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 5

A man deposits ₹

37, 000

in three banks at the rate of

4 %, 5 % and 6 %

simple interest. If he gets an equal amount of interest from each bank, then what are the amounts he deposited in each bank ?

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 6

Solve:

$\frac{x - 3}{x + 3} + \frac{x + 3}{x - 3} = 2 \frac{1}{2}$

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 6

The length of the hypotenuse of a right-angled triangle is $6 c m$ more than twice the least side. If the length of the third side is $2 c m$ less than the hypotenuse, then what are the length of three sides of the triangle ?

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 7

If $\frac{4 \sqrt{3}}{2 - \sqrt{2}} - \frac{30}{4 \sqrt{3} - \sqrt{18}} - \frac{\sqrt{18}}{3 - \sqrt{12}} = a \sqrt{b}$ , then find the value of $a + b$