The image contains three different questions involving triangles:

Question 2

Q2: Find the area of each of the triangles shown below. Each base and height is measured in decimal places.

• First Triangle:
  • Base: 2.9 cm
  • Height: 1.5 cm
• Second Triangle:
  • Base: 4.2 cm
  • Height: 2.8 cm
• Third Triangle:
  • Base: 5.3 cm
  • Height: 4.1 cm

Formula to use: Area of a triangle = $\frac{1}{2} \times \text{Base} \times \text{Height}$

Question 3

Q3: Find the area of each of the triangles shown below. Each base and height is measured in decimal places.

• First Triangle:
  • Base: 6.7 cm
  • Height: 3.4 cm
• Second Triangle:
  • Base: 5.1 cm
  • Height: 2.5 cm
• Third Triangle:
  • Base: 8.6 cm
  • Height: 4.5 cm

Formula to use: Area of a triangle = $\frac{1}{2} \times \text{Base} \times \text{Height}$

Question 4

Q4: Find the area of each of the triangles below in square units. Find the missing area by using either $\frac{1}{2} \times \text{base} \times \text{height}$ or $\text{Area} = \frac{ab \sin(C)}{2}$.

• First Triangle:
  • Side a: 6.3 cm
  • Side b: 9.2 cm
  • Angle C: 51°
• Second Triangle:
  • Side a: 8.1 cm
  • Side b: 10.4 cm
  • Angle C: 37°

Let's solve each problem step-by-step.

Solutions

1. Q2 - Area Calculations:

   • First Triangle: Area = $\frac{1}{2} \times 2.9 \times 1.5$ cm²
   • Second Triangle: Area = $\frac{1}{2} \times 4.2 \times 2.8$ cm²
   • Third Triangle: Area = $\frac{1}{2} \times 5.3 \times 4.1$ cm²

2. Q3 - Area Calculations:

   • First Triangle: Area = $\frac{1}{2} \times 6.7 \times 3.4$ cm²
   • Second Triangle: Area = $\frac{1}{2} \times 5.1 \times 2.5$ cm²
   • Third Triangle: Area = $\frac{1}{2} \times 8.6 \times 4.5$ cm²

3. Q4 - Area Calculations using Trigonometric Formula:

   • First Triangle: Area = $\frac{1}{2} \times 6.3 \times 9.2 \times \sin(51^\circ)$
   • Second Triangle: Area = $\frac{1}{2} \times 8.1 \times 10.4 \times \sin(37^\circ)$

Let's perform these calculations:Here are the calculated areas for each triangle:

Q2 - Triangle Areas

1. First Triangle: Area = 2.17 cm²
2. Second Triangle: Area = 5.88 cm²
3. Third Triangle: Area = 10.86 cm²

Q3 - Triangle Areas

1. First Triangle: Area = 11.39 cm²
2. Second Triangle: Area = 6.38 cm²
3. Third Triangle: Area = 19.35 cm²

Q4 - Triangle Areas using Trigonometric Formula

1. First Triangle: Area = 22.52 cm²
2. Second Triangle: Area = 25.35 cm²

Would you like any further details on these calculations, or do you have any other questions?

Related Questions

1. How do you calculate the area of a triangle using the sine formula?
2. What are the differences between calculating the area of a triangle with the base-height method versus using trigonometry?
3. How do you convert degrees to radians when using trigonometric functions?
4. How does changing one angle affect the area of a triangle?
5. Can the sine formula be used for all types of triangles?

Tip:

Always double-check the angle measurement mode (degrees vs. radians) when using trigonometric functions on a calculator or in programming to avoid errors in calculations.