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Ask QuestionPosted by Charanjit Singh 4 years, 10 months ago
- 2 answers
Yogita Ingle 4 years, 10 months ago
Given a quadrilateral ABCD in which ∠C = 90º, AB = 9 m, BC = 12 m, CD = 5 m & AD = 8 m.
Join the diagonal BD which divides quadrilateral ABCD in two triangles i.e ∆BCD & ∆ABD.
In ΔBCD,
By applying Pythagoras Theorem
BD²=BC² +CD²
BD²= 12²+ 5²= 144+25
BD²= 169
BD = √169= 13m
∆BCD is a right angled triangle.
Area of ΔBCD = 1/2 ×base× height
=1/2× 5 × 12= 30 m²
For ∆ABD,
Let a= 9m, b= 8m, c=13m
Now,
Semi perimeter of ΔABD,(s) = (a+b+c) /2
s=(8 + 9 + 13)/2 m
= 30/2 m = 15 m
s = 15m
Using heron’s formula,
Area of ΔABD = √s (s-a) (s-b) (s-c)
= √15(15 – 9) (15 – 9) (15 – 13)
= √15 × 6 × 7× 2
=√5×3×3×2×7×2
=3×2√35
= 6√35= 6× 5.92
[ √6= 5.92..]
= 35.52m² (approx)
Area of quadrilateral ABCD = Area of ΔBCD + Area of ΔABD
= 30+ 35.5= 65.5 m²
Hence, area of the park is 65.5m²
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Yogita Ingle 4 years, 10 months ago
Given: ABCD is a parallelogram. AE bisects ∠BAD. BF bisects ∠ABC. CG bisects ∠BCD and DH bisects ∠ADC
To prove: LKJI is a rectangle
∠BAD + ∠ABC = 180° because adjacent angles of a parallelogram are supplementary
ΔABJ is a right triangle since its acute interior angles are complementary
Similar in ΔCDL we get ∠DLC = 90° and in ΔADI we get ∠AID = 90°
Then ∠JIL = 90° as ∠AID and ∠JIL are vertical opposite angles
Since three angles of quadrilateral LKJI are right angles, hence 4th angle is also a right angle.
Thus LKJI is a rectangle.
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- 2 answers
Yogita Ingle 4 years, 10 months ago
It is defined as the values of all the trigonometric function based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
- sine: Sine of an angle is defined as the ratio of the side opposite(perpendicular side) to that angle to the hypotenuse.
- cosine: Cosine of an angle is defined as the ratio of the side adjacent to that angle to the hypotenuse.
- tangent: Tangent of an angle is defined as the ratio of the side opposite to that angle to the side adjacent to that angle.
- cosecant: Cosecant is a multiplicative inverse of sine.
- secant: Secant is a multiplicative inverse of cosine.
- cotangent: Cotangent is the multiplicative inverse of the tangent.
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Yogita Ingle 4 years, 10 months ago
First 10 prime numbers are 2,3,5,7,11,13,17,19,23,27.
Median = value of (n/2)th observation + value of(n/2 + 1) observation/2
= value of 5th observation + value of 6th observation/2
= 11+13/2
= 24/2
= 12
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Smita Malvankar 4 years, 10 months ago
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