We read your photo as:

A right-angled triangle has an opposite side of 3 cm and an adjacent side of 4 cm. Calculate sinθ and identify the correct option.

Mathematics

ScanSolve AI Answer

Step-by-step solution

7 steps

  1. Find the hypotenuse of the right-angled triangle.

    Given the opposite side is 3 cm3 \text{ cm} and the adjacent side is 4 cm4 \text{ cm}.
    Using the Pythagorean theorem, a2+b2=c2a^2 + b^2 = c^2, where cc is the hypotenuse.

    hypotenuse=(opposite)2+(adjacent)2\text{hypotenuse} = \sqrt{(\text{opposite})^2 + (\text{adjacent})^2} hypotenuse=(3 cm)2+(4 cm)2\text{hypotenuse} = \sqrt{(3 \text{ cm})^2 + (4 \text{ cm})^2} hypotenuse=9 cm2+16 cm2\text{hypotenuse} = \sqrt{9 \text{ cm}^2 + 16 \text{ cm}^2} hypotenuse=25 cm2\text{hypotenuse} = \sqrt{25 \text{ cm}^2} hypotenuse=5 cm\text{hypotenuse} = 5 \text{ cm}

  2. Calculate sin⁡θ\sin\theta.

    The definition of sin⁡θ\sin\theta in a right-angled triangle is the ratio of the length of the opposite side to the length of the hypotenuse.

    sin⁡θ=oppositehypotenuse\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}} sin⁡θ=3 cm5 cm\sin\theta = \frac{3 \text{ cm}}{5 \text{ cm}} sin⁡θ=35\sin\theta = \frac{3}{5}

  3. Compare with the given options.

    The calculated value 35\frac{3}{5} matches option C.

    The final answer is C\boxed{\text{C}}.

  4. Convert the actual distance to centimeters.

    The map distance is 12 cm12 \text{ cm}.
    The actual distance is 36 km36 \text{ km}.
    We know that 1 km=1000 m1 \text{ km} = 1000 \text{ m} and 1 m=100 cm1 \text{ m} = 100 \text{ cm}.
    Therefore, 1 km=1000×100 cm=100,000 cm1 \text{ km} = 1000 \times 100 \text{ cm} = 100,000 \text{ cm}.
    So, 36 km=36×100,000 cm=3,600,000 cm36 \text{ km} = 36 \times 100,000 \text{ cm} = 3,600,000 \text{ cm}.

  5. Express the scale as a ratio of map distance to actual distance.

    The scale is given by:

    Scale=Map distance:Actual distance\text{Scale} = \text{Map distance} : \text{Actual distance} Scale=12 cm:3,600,000 cm\text{Scale} = 12 \text{ cm} : 3,600,000 \text{ cm}

  6. Simplify the ratio to the form $1:N$.

    Divide both sides of the ratio by 12:

    Scale=1212:3,600,00012\text{Scale} = \frac{12}{12} : \frac{3,600,000}{12} Scale=1:300,000\text{Scale} = 1 : 300,000

  7. Compare with the given options.

    The calculated scale 1:3000001:300000 matches option A.

    The final answer is A\boxed{\text{A}}.

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QDefine sin θ in a right-angled triangle. 2. Calculate tan 60°. 3. Given cot θ = 12/5 and 180° < θ…QIdentify the angle and the sides of the right-angled triangle.QThe hypotenuse of a right-angled triangle is 12 cm. The side opposite to angle M is 9 cm. Find the…QIdentify the relevant right-angled triangle.QGiven theta = (1)/(3). We can construct a right-angled triangle where the opposite side is 1 and the…
Browse by topic:GeometryTrigonometry
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp