Math Problem Statement

Jawablah soal diatas

Jawablah soal diatas

Solution

The questions on this worksheet relate to the Pythagorean theorem and properties of special right triangles (30°-60°-90° and 45°-45°-90° triangles). Let’s go through each section systematically to provide solutions.

Section 1: Teori Segitiga Istimewa 30° dan 60°

Given a right triangle with:

  • Hypotenuse AC=18AC = 18 cm
  • Angle BAC=30\angle BAC = 30^\circ and ACB=60\angle ACB = 60^\circ

From the properties of a 30°-60°-90° triangle:

  1. The side opposite 30° (BC) is half the hypotenuse: BC=12×AC=12×18=9 cmBC = \frac{1}{2} \times AC = \frac{1}{2} \times 18 = 9 \text{ cm}

  2. The side opposite 60° (AB) is 32×AC\frac{\sqrt{3}}{2} \times AC: AB=32×18=9315.6 cmAB = \frac{\sqrt{3}}{2} \times 18 = 9\sqrt{3} \approx 15.6 \text{ cm}

Solutions:

  • Panjang BC=9BC = 9 cm
  • Panjang AB=15.6AB = 15.6 cm (rounded to 1 decimal place)

Section 2: Teori Segitiga Istimewa 45°

Given a 45°-45°-90° triangle:

  1. If one leg (e.g., PR=7PR = 7 cm), the hypotenuse PQPQ is 2\sqrt{2} times the leg: QR=PR×2=7×29.9 cmQR = PR \times \sqrt{2} = 7 \times \sqrt{2} \approx 9.9 \text{ cm}

Solutions:

  • Panjang QR9.9QR \approx 9.9 cm (rounded to 1 decimal place)

LATIHAN LKPD 07

For this part, it provides two triangle problems.

Question 1

Given triangle ABCABC:

  • AB=203=34.6AB = 20 \sqrt{3} = 34.6 cm

Solution Steps:

  1. BAC\angle BAC: Calculate angle based on known values (usually involves trig functions).
  2. BDBD: Using Pythagorean theorem or triangle properties.
  3. ADAD: Relation between parts using triangle properties.
  4. ACAC: Calculation based on properties of right triangles.

Question 2

Properties and area calculations of triangle ABCABC, given data to solve each geometric property.


Would you like a detailed solution for each sub-question in LATIHAN LKPD 07? Here are some related questions:

  1. How do you determine side lengths in a 30°-60°-90° triangle?
  2. How is the hypotenuse calculated in a 45°-45°-90° triangle?
  3. How can trigonometric functions be used to find angles?
  4. What is the formula for the area of a right triangle?
  5. How to apply the Pythagorean theorem in non-right triangles?

Tip: Remember that the 30°-60°-90° triangle has specific side ratios (1 : √3 : 2), which can simplify many calculations.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Pythagorean Theorem
Special Right Triangles (30°-60°-90° and 45°-45°-90°)
Trigonometry in Right Triangles
Area Calculation of Triangles

Formulas

Pythagorean Theorem: a^2 + b^2 = c^2
30°-60°-90° triangle side ratios: 1 : √3 : 2
45°-45°-90° triangle side ratios: 1 : 1 : √2
Area of Triangle: (1/2) * base * height

Theorems

Pythagorean Theorem
Properties of 30°-60°-90° Triangles
Properties of 45°-45°-90° Triangles

Suitable Grade Level

Grades 9-10