To find the straight-line distance from Manish's office to his home, we need to determine his net displacement in the East-West and North-South directions. We can break down his movements step by step:

Step 1: Analyze Manish's Movements

• Manish starts at his office facing North.
• He walks 15 m to his right. Since he is facing North, his right is East. Movement: 15 m East.
• He turns to his left and walks 23 m. Facing East, turning left means he now faces North. Movement: 23 m North.
• He turns to his right and walks 6 m. Facing North, turning right means he now faces East. Movement: 6 m East.
• He turns to his right and walks 43 m. Facing East, turning right means he now faces South. Movement: 43 m South.

Step 2: Calculate Net Displacement

We calculate the total displacement along the East-West axis and the North-South axis separately.

East-West Displacement:

Manish moved East twice:

• First movement East = 15 m
• Second movement East = 6 m
• Total Eastward Displacement = $15 \text{ m} + 6 \text{ m} = 21 \text{ m}$

North-South Displacement:

Manish moved North once and South once:

• Movement North = 23 m
• Movement South = 43 m
• Net Southward Displacement = $43 \text{ m} - 23 \text{ m} = 20 \text{ m}$
• (This means he ended up 20 m South of his starting North-South position).

Step 3: Visualize the Final Position

Manish's final position is 21 m East and 20 m South relative to his starting point (office). This forms a right-angled triangle where:

• One leg is the net Eastward displacement (21 m).
• The other leg is the net Southward displacement (20 m).
• The hypotenuse is the straight-line distance from his office to his home.

Step 4: Calculate the Straight-Line Distance

We use the Pythagorean theorem to find the distance (hypotenuse):

Distance$^2$ = (Eastward Displacement)$^2$ + (Southward Displacement)$^2$

Distance$^2$ = $(21 \text{ m})^2 + (20 \text{ m})^2$

Distance$^2$ = $441 \text{ m}^2 + 400 \text{ m}^2$

Distance$^2$ = $841 \text{ m}^2$

Distance = $\sqrt{841 \text{ m}^2}$

Distance = $29 \text{ m}$

Conclusion

The straight-line distance Manish will have to walk from his office to his home is 29 m.