SSC (Marathi Semi-English) १० वीं कक्षा - Maharashtra State Board Question Bank Solutions for Geometry Mathematics 2

If cos(45° + x) = sin 30°, then x = ?

If sec A = `x + 1/(4x)`, then show that sec A + tan A = 2x or `1/(2x)`

In the above figure `square`ABCD is a rectangle. If AB = 5, AC = 13, then complete the following activity to find BC.

Activity: ΔABC is a `square` triangle.

∴ By Pythagoras theorem

AB² + BC² = AC²

∴ 25 + BC² = `square`

∴ BC² = `square`

∴ BC = `square`

Construct two concentric circles with centre O with radii 3 cm and 5 cm. Construct a tangent to a smaller circle from any point A on the larger circle. Measure and write the length of the tangent segment. Calculate the length of the tangent segment using Pythagoras' theorem.

In the right-angled triangle ABC, Hypotenuse AC = 10 and side AB = 5, then what is the measure of ∠A?

If tan θ = `12/5`, then 5 sin θ – 12 cos θ = ?

From the information in the figure, complete the following activity to find the length of the hypotenuse AC.

AB = BC = `square`

∴ ∠BAC = `square`

Side opposite angle 45° = `square/square` × Hypotenuse

∴ `5sqrt(2) = 1/square` × AC

∴ AC = `5sqrt(2) xx square = square`

AB, BC and AC are three sides of a right-angled triangle having lengths 6 cm, 8 cm and 10 cm, respectively. To verify the Pythagoras theorem for this triangle, fill in the boxes:

ΔABC is a right-angled triangle and ∠ABC = 90°.

So, by the Pythagoras theorem,

`square` + `square` = `square`

Substituting 6 cm for AB and 8 cm for BC in L.H.S.

`square` + `square` = `square` + `square`

= `square` + `square`

= `square`

Substituting 10 cm for AC in R.H.S.

`square` = `square`

= `square`

Since, L.H.S. = R.H.S.

Hence, the Pythagoras theorem is verified.

There is a ladder of length 32 m which rests on a pole. If the height of pole is 18 m, determine the distance between the foot of ladder and the pole.

A person starts his trip from home. He moves 24 km in south direction and then starts moving towards east. He travels 7 km in that direction and finally reaches his destination. How far is the destination from his home?

Find the side of a square whose diagonal is `10sqrt2` cm.

Using Euler’s formula, find V if E = 30, F = 12.

For the angle in standard position if the initial arm rotates 25° in anticlockwise direction, then state the quadrant in which terminal arm lies (Draw the figure and write the answer).

In the following figure seg AB ⊥ seg BC, seg DC ⊥ seg BC. If AB = 2 and DC = 3, find `(A(triangleABC))/(A(triangleDCB))`

The ratio of the areas of two triangles with the common base is 14 : 9. Height of the larger triangle is 7 cm, then find the corresponding height of the smaller triangle.

Write down the equation of a line whose slope is 3/2 and which passes through point P, where P divides the line segment AB joining A(-2, 6) and B(3, -4) in the ratio 2 : 3.

ΔRST ~ ΔUAY, In ΔRST, RS = 6 cm, ∠S = 50°, ST = 7.5 cm. The corresponding sides of ΔRST and ΔUAY are in the ratio 5 : 4. Construct ΔUAY.

In the following figure RP : PK= 3 : 2, then find the value of A(ΔTRP) : A(ΔTPK).

Construct the circumcircle and incircle of an equilateral triangle ABC with side 6 cm and centre O. Find the ratio of radii of circumcircle and incircle.

Find the distance between the following pairs of points:

(2, 3), (4, 1)